{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Merton Partial Integro-Differential Equation\n",
    "\n",
    "## Contents\n",
    "   - [The Merton PIDE](#sec1)\n",
    "      - [Discretization](#sec1.1)\n",
    "   - [Numerical solution of the PIDE](#sec2)\n",
    "   - [Comparison with Monte Carlo and closed formula](#sec3)\n",
    "   - [Model limitations](#sec4)\n",
    "   - [Comparison with the Black Scholes PDE](#sec5)  \n",
    "   \n",
    "   \n",
    "The notebook **2.1** is a prerequisites for understanding this notebook. If you don't know the Merton model, have a look at the notebook **A.3**.\n",
    "\n",
    "In this notebook we only consider the problem of solving the Merton PIDE.    \n",
    "Let us recall that, this is the pricing PIDE associated to the process:   \n",
    "\n",
    "\\begin{equation}\\label{MertonM}\n",
    "X_t = \\mu t + \\sigma W_t + \\sum_{i=1}^{N_t} Y_i, \n",
    "\\end{equation}\n",
    "\n",
    "where $N_t$ is a Poisson random variable representing the number of jumps of $X_t$ up to time $t$, and $Y_i \\sim \\mathcal{N}(\\alpha, \\xi^2)$ is the size of each jump. (more details in **A.3**)\n",
    "\n",
    "This is an **incomplete model**. It means that the risk neutral measure is not unique (for more information see Section 3 of **A.3** or the [wiki page](https://en.wikipedia.org/wiki/Fundamental_theorem_of_asset_pricing)).    \n",
    "In the following, we will adopt the choice (proposed by Merton) that, when changing from the physical to the risk neutral measure, only the drift is changed, while the other ingredients are unchanged.    \n",
    "The risk neutral process has drift:\n",
    "\n",
    "$$ \\mu = r - \\frac{1}{2} \\sigma^2 - m $$\n",
    " \n",
    "with $r$ risk free interest rate, and $m$ defined below.\n",
    "\n",
    "##### Closed formula\n",
    "Just for information, there exists a closed formula for pricing European call/put options under the Merton model.\n",
    "This formula was presented by Merton in [2]. We just report it without derivation.\n",
    "\n",
    "$$ \\sum_k \\frac{e^{-\\psi T} \\psi T}{k!} \\; V^{BS}\\biggl( S_0,\\, T,\\, r - m + \\frac{k (\\alpha + \\xi^2/2)}{T}  ,\\, \\sqrt{\\sigma^2 + \\frac{k \\xi^2}{T}} \\biggr)  $$ \n",
    "\n",
    "with $\\psi = \\lambda \\bigl( e^{\\alpha + \\frac{1}{2} \\xi^2} \\bigr)$, and $V^{BS}(S,T,r,\\sigma)$ is the Black-Scholes closed formula."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec1'></a>\n",
    "## The Merton PIDE\n",
    "\n",
    "In this notebook I want to show how to solve the Merton PIDE:   \n",
    "\n",
    "\\begin{align}\n",
    "  \\frac{\\partial V(t,x)}{\\partial t}\n",
    "          + \\biggl( r -\\frac{1}{2}\\sigma^2 -m \\biggr) \\frac{\\partial V(t,x)}{\\partial x}\n",
    "          + \\frac{1}{2} \\sigma^2 \\frac{\\partial^2 V(t,x)}{\\partial x^2} \n",
    "          + \\int_{\\mathbb{R}} V(t,x+z) \\nu(dz) - (\\lambda+r) V(t,x)  = 0.\n",
    "\\end{align}\n",
    "\n",
    "with\n",
    "\\begin{align} \n",
    " m :=& \\; \\int_{\\mathbb{R}} ( e^{z} - 1 ) \\nu(dz) \\\\\n",
    "    =& \\; \\lambda \\biggl( e^{\\alpha + \\frac{1}{2} \\xi^2} -1 \\biggr).\n",
    "\\end{align}\n",
    "\n",
    "The Lévy measure is:\n",
    "$$ \\nu(dz) = \\frac{\\lambda}{\\xi \\sqrt{2\\pi}} e^{- \\frac{(z-\\alpha)^2}{2\\xi^2}} dz.  $$\n",
    "\n",
    "The Lévy measure is a scaled Normal distribution, such that $\\lambda = \\int_{\\mathbb{R}} \\nu(dz)$.\n",
    "\n",
    "For more information on the derivation of this PIDE, have a look at the document **A.3**. It includes a short introduction to general pricing PIDEs and the description of the Merton model.   \n",
    "\n",
    "This equation is an \"extension\" of the Black-Scholes equation. It coincides with the BS equation for $\\lambda = 0$.\n",
    "\n",
    "Let us first introduce the discretization method, and then write everything in python!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec1.1'></a>\n",
    "### Discretization\n",
    "\n",
    "The discretization of this equation is quite similar to the discretization of the BS equation.   \n",
    "However, here there is an additional integral term!!\n",
    "\n",
    "We will adopt the Implicit-Explicit **(IMEX)** scheme proposed by Cont-Voltchkova [1]. The differential part is discretized by an implicit scheme (the same approach used for the BS equation). The integral part in instead discretized by an explicit scheme. The reason of the explicit choice, is that it avoids the inversion of the dense \"jump\" matrix (below we will construct the jump matrix).\n",
    "\n",
    "The integral part is computed using **fourier methods** (it is a convolution integral) in order to increasing the efficiency."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we have to restrict the problem to a bounded region, we consider the equation:  \n",
    "\n",
    "\\begin{align*}\n",
    "  \\frac{\\partial V(t,x)}{\\partial t} \n",
    "          + \\biggl( r -\\frac{1}{2}\\sigma^2 - \\hat m \\biggr) \\frac{\\partial V(t,x)}{\\partial x} \n",
    "          + \\frac{1}{2} \\sigma^2 \\frac{\\partial^2 V(t,x)}{\\partial x^2} \n",
    "          + \\int_{-B_1}^{B_2} V(t,x+z) \\nu(dz) - (\\hat \\lambda + r) V(t,x)  = 0.\n",
    "\\end{align*}\n",
    "\n",
    "with   \n",
    "\n",
    "$$ \\hat m = \\int_{-B_1}^{B_2} \\bigl( e^z-1 \\bigr) \\nu(dz)$$ \n",
    "and \n",
    "$$\\hat \\lambda = \\int_{-B_1}^{B_2} \\nu(dz).$$\n",
    "\n",
    "For $0 < K_1 < K_2$ we choose $B_1,B_2$ such that $ \\bigl[-B_1,B_2\\bigr] = \\bigl[ ( -K_1-1/2 )\\Delta x , ( K_2+1/2 )\\Delta x \\bigr] $, and $\\Delta x$ is the space step.  \n",
    "\n",
    "The computational domain of interest becomes $[0,T]\\, \\times \\, [A_1-B_1,A_2+B_2]$, where in the regions $[0,T]\\, \\times \\, [A_1-B_1,A_1]$ and \n",
    "$[0,T]\\, \\times \\, [A_2,A_2+B_2]$ we need to define the boundary conditions.\n",
    "\n",
    "Let us discretize the integral as follows:\n",
    "\n",
    "$$ \\int_{-B_1}^{B_2}  V(t_n,x_i+z) \\nu(dz) \\approx \\sum_{k = -K_1}^{K_2} \\nu_k V^{n}_{i+k} $$\n",
    "\n",
    "where\n",
    "\n",
    "$$\n",
    " \\nu_k = \\int_{(k-\\frac{1}{2}) \\Delta x}^{(k+\\frac{1}{2}) \\Delta x} \\nu(z) dz, \\hspace{1em} \\mbox{ for } \\hspace{1em} -K_1 \\leq k \\leq K_2. \n",
    "$$\n",
    "\n",
    "We have that $ \\hat \\lambda = \\sum_{k = -K_1}^{K_2} \\nu_k $. For large values of $B_1$ and $B_2$, the parameter $\\hat \\lambda$ is a good approximation for $\\lambda$, since\n",
    "\n",
    "$$\\lambda = \\lim_{B_1,B_2 \\to \\infty} \\hat \\lambda = \\lim_{B_1,B_2 \\to \\infty} \\int_{-B_1}^{B_2} \\nu(dz). $$\n",
    "\n",
    "The discretized equation using the IMEX scheme becomes:   \n",
    "\n",
    "$$ \\begin{aligned}\n",
    "&\\frac{V^{n+1}_{i} -V^{n}_{i}}{\\Delta t} + \n",
    "(r-\\frac{1}{2}\\sigma^2 - \\hat m) \\frac{V^{n}_{i+1} -V^{n}_{i-1}}{ 2 \\Delta x} \\\\ \\nonumber\n",
    "&+ \\frac{1}{2} \\sigma^2 \\frac{V^{n}_{i+1} + V^{n}_{i-1} - 2 V^{n}_{i}}{\\Delta x^2}  - (r+\\hat \\lambda) V^{n}_i +\\sum_{k = -K_1}^{K_2} \\nu_k V^{n+1}_{i+k} = 0.\n",
    "\\end{aligned} $$\n",
    "\n",
    "Rearranging the terms: \n",
    "\n",
    "$$ \\begin{aligned}\n",
    "\\underbrace{ V^{n+1}_{i} + \\Delta t \\sum_{k = -K_1}^{K_2} \\nu_k V^{n+1}_{i+k} }_{\\tilde V^{n+1}_i} &= \n",
    "\tV^{n}_{i} \\biggl( 1 + (r+\\hat \\lambda)\\Delta t + \\sigma^2 \\frac{\\Delta t}{\\Delta x^2} \\biggr)  \\\\\n",
    "& + V^{n}_{i+1} \\biggl( -(r -\\frac{1}{2}\\sigma^2 -\\hat m )\\frac{\\Delta t}{2 \\Delta x} +\n",
    "\\frac{1}{2}\\sigma^2 \\frac{\\Delta t}{\\Delta x^2}  \\biggr)  \\\\\n",
    "& + V^{n}_{i-1} \\biggl( (r -\\frac{1}{2}\\sigma^2 - \\hat m)\\frac{\\Delta t}{2 \\Delta x} + \n",
    "\\frac{1}{2}\\sigma^2 \\frac{\\Delta t}{\\Delta x^2}  \\biggr).\n",
    "\\end{aligned} $$\n",
    "\n",
    "We can rename the coefficients:\n",
    "\n",
    "$$ \\tilde V^{n+1}_{i} = a V^{n}_{i-1} + b V^{n}_{i} + c V^{n}_{i+1}, $$\n",
    "\n",
    "and solve the system for $V^{n}_{i}$,  for every $1 \\leq i \\leq M-1$:\n",
    "\n",
    "$$\n",
    " \\begin{cases}\n",
    "  \\tilde V^{n+1}_i = V^{n+1}_{i} + \\Delta t \\sum_{k = -K_1}^{K_2} V^{n+1}_{i+k} \\nu_k \\quad \\mbox{ for } \\quad 1 \\leq i \\leq M-1 \\\\\n",
    "  V^{n} = \\mathcal{D}^{-1} \\biggl( \\tilde V^{n+1} - B \\biggr)   \n",
    " \\end{cases}\n",
    "$$\n",
    "\n",
    "where $\\mathcal{D}$ is the tridiagonal matrix formed by the coefficients $a,b,c$, and with boundary terms $B = (a V^{n}_{0}, 0, ... , 0, c V^{n}_{M})$.  \n",
    "\n",
    "Introducing the *jump* matrix $J$, the system becomes:\n",
    "\n",
    "$$\n",
    " \\begin{cases}\n",
    "  \\tilde V^{n+1} = V^{n+1} + \\Delta t \\, J \\, V^{n+1} \\\\\n",
    "  V^{n} = \\mathcal{D}^{-1} \\biggl( \\tilde V^{n+1} - B \\biggr) %\\quad \\mbox{ for } \\quad 1 \\leq i \\leq M-1.  \n",
    " \\end{cases}\n",
    "$$\n",
    "\n",
    "However, we will see that it is better to avoid to use this matrix, and solve the integral by **fft** methods."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec2'></a>\n",
    "## Numerical solution of the PIDE\n",
    "\n",
    "Ok... we are ready to implement the previous algorithm.  \n",
    "\n",
    "In order to have a clear presentation, I prefer to choose a small number of time and space steps. It will be easier for you to follow what I'm doing.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import sparse\n",
    "from scipy.sparse.linalg import splu\n",
    "\n",
    "import numpy as np\n",
    "import scipy as scp\n",
    "import scipy.stats as ss\n",
    "from IPython.display import display\n",
    "import sympy; sympy.init_printing()\n",
    "from scipy import signal\n",
    "from scipy.integrate import quad\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def display_matrix(m):\n",
    "    display(sympy.Matrix(m))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = 0.1; sig = 0.2          # risk free rate and diffusion coefficient      \n",
    "S0 = 100; X0 = np.log(S0)   # spot price and log-price       \n",
    "K = 100; Texpir = 1         # strike and maturity            \n",
    "\n",
    "lam = 0.8   # lambda \n",
    "muJ = 0     # (or alpha) is the mean of the jump size \n",
    "sigJ = 0.5  # (or xi) is the standard deviation of the jump size \n",
    "\n",
    "Nspace = 5   # M space steps \n",
    "Ntime = 3    # N time steps \n",
    "S_max = 3*float(K)                \n",
    "S_min = float(K)/3\n",
    "x_max = np.log(S_max)  # A2\n",
    "x_min = np.log(S_min)  # A1\n",
    "\n",
    "dev_X = np.sqrt(lam * sigJ**2 + lam * muJ**2)   # std dev of the jump component\n",
    "\n",
    "dx = (x_max - x_min)/(Nspace-1)\n",
    "extraP = int(np.floor(3*dev_X/dx))  # extra points\n",
    "x = np.linspace(x_min-extraP*dx, x_max+extraP*dx, Nspace + 2*extraP)   # space discretization\n",
    "T, dt = np.linspace(0, Texpir, Ntime, retstep=True)       # time discretization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What I did was: \n",
    "- define tha parameters. \n",
    "  I called muJ and sigJ the mean and standard deviation of the (normal) jump random variables. They correspond to        $\\alpha$ and $\\xi$. \n",
    "- obtain the boundary values: A1 and A2. And the space step *dx* and time step *dt*.\n",
    "  The variable `x` takes values in the extended computational domain $[A_1-B_1, A_2+B_2]$. \n",
    "- compute the standard deviation of the jump component (at $t=1$). Let us recall the variance formula for the compound Poisson process (obtained from the formula of conditional variance):\n",
    "$$ Var \\biggl[ \\sum_{i=1}^{N_t} Y_i \\biggr] = \\lambda (\\alpha^2 + \\xi^2) t $$\n",
    "- compute the extra points *extraP* indicating the number of points to use as extra bounday conditions. The extra points are the points in the regions $[A_1 - B_1, A_1]$ and $[A_2, A_2 + B_2]$.\n",
    "\n",
    "Why did I choose the extra points in that way?\n",
    "\n",
    "The idea is that we want to cover at least 3 standard deviations of the domain of the Lévy measure. The choice of 3 is arbitrary. The higher is the better.     \n",
    "The important fact to remember, is that the smaller is $\\Delta X$, the higher is *extraP*. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Under this discretization there are 2 extra points\n"
     ]
    }
   ],
   "source": [
    "print(\"Under this discretization there are {} extra points\".format(extraP))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 73.21\\\\209.52 & 204.88 & 200.0\\\\429.13 & 424.49 & 419.62\\\\809.52 & 804.88 & 800.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡ 0.0     0.0     0.0  ⎤\n",
       "⎢                      ⎥\n",
       "⎢ 0.0     0.0     0.0  ⎥\n",
       "⎢                      ⎥\n",
       "⎢ 0.0     0.0     0.0  ⎥\n",
       "⎢                      ⎥\n",
       "⎢ 0.0     0.0     0.0  ⎥\n",
       "⎢                      ⎥\n",
       "⎢ 0.0     0.0     0.0  ⎥\n",
       "⎢                      ⎥\n",
       "⎢ 0.0     0.0    73.21 ⎥\n",
       "⎢                      ⎥\n",
       "⎢209.52  204.88  200.0 ⎥\n",
       "⎢                      ⎥\n",
       "⎢429.13  424.49  419.62⎥\n",
       "⎢                      ⎥\n",
       "⎣809.52  804.88  800.0 ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Payoff = np.maximum(np.exp(x)-K,0)             # Call payoff\n",
    "V = np.zeros((Nspace + 2*extraP, Ntime))       # grid initialization\n",
    "offset = np.zeros(Nspace-2)        # vector to be used for the boundary terms\n",
    "\n",
    "V[:,-1] = Payoff                   # terminal conditions \n",
    "V[-extraP-1:,:] = np.exp(x[-extraP-1:]).reshape(extraP+1,1) * np.ones((extraP+1,Ntime)) - \\\n",
    "                 K * np.exp(-r* T[::-1] ) * np.ones((extraP+1,Ntime))  # boundary conditions for the call  \n",
    "V[:extraP+1,:] = 0\n",
    "\n",
    "display_matrix(V.round(2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the previous cell we created the grid for $V$.     \n",
    "The time grows from left to right. The stock price grows from up to down.\n",
    "\n",
    "- The first 2 rows, and the last 2, are the extra boundary conditions. (In agreement with extraP)\n",
    "- The third row and the seventh row are the usual boudary conditions.\n",
    "- The last column corresponds to the terminal boundary condition."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us create the vector $\\nu_k$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.00236098 0.03733859 0.19337038 0.3337637  0.19337038 0.03733859\n",
      " 0.00236098]\n"
     ]
    }
   ],
   "source": [
    "cdf = ss.norm.cdf([np.linspace(-(extraP+1+0.5)*dx, (extraP+1+0.5)*dx, 2*(extraP+2) )], loc=muJ, scale=sigJ)[0]\n",
    "nu = lam * (cdf[1:] - cdf[:-1])\n",
    "print(nu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The integral:\n",
    "$$ \\hat m = \\int_{-B_1}^{B_2} \\bigl( e^z-1 \\bigr) \\nu(dz)$$ \n",
    "can be computed using two methods:\n",
    "- or using the scipy function `quad`\n",
    "- or using the discretization:\n",
    "$$  \\hat m \\approx \\sum_{k = -K_1}^{K_2} (e^{k \\Delta x}-1) \\nu_k  $$\n",
    "\n",
    "These two methods are equivalent. We show both in the next cell. Of course the values are different because $\\Delta x$ is quite big now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Truncated jump activity:  0.7999036142791525\n",
      "True value:  0.10651876245346106\n",
      "Truncated value, using quad:  0.10623607827426487\n",
      "Approximation value:  0.11761420996944338\n"
     ]
    }
   ],
   "source": [
    "lam_appr = sum(nu)    # sum of the components of nu\n",
    "print(\"Truncated jump activity: \", lam_appr)\n",
    "\n",
    "m = lam * (np.exp(muJ + (sigJ**2)/2) -1)     # coefficient m\n",
    "print(\"True value: \", m)\n",
    "m_int = quad(lambda z: lam * (np.exp(z)-1) * ss.norm.pdf(z,muJ,sigJ), -(extraP+1.5)*dx, (extraP+1.5)*dx )[0]\n",
    "print(\"Truncated value, using quad: \", m_int)\n",
    "m_appr = np.array([ np.exp(i*dx)-1 for i in range(-(extraP+1), extraP+2)]) @ nu\n",
    "print(\"Approximation value: \", m_appr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# construction of the tri-diagonal matrix D\n",
    "sig2 = sig*sig; dxx = dx * dx\n",
    "a = ( (dt/2) * ( (r-m_appr-0.5*sig2)/dx - sig2/dxx ) )\n",
    "b = ( 1 + dt * ( sig2/dxx + r + lam_appr) )\n",
    "c = (-(dt/2) * ( (r-m_appr-0.5*sig2)/dx + sig2/dxx ) )\n",
    "D = sparse.diags([a, b, c], [-1, 0, 1], shape=(Nspace-2, Nspace-2)).tocsc()\n",
    "DD = splu(D)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the previous cell we created the \"diffusion\" matrix, in the same way we did for the Black-Scholes equation in the notebook **2.1**.\n",
    "\n",
    "In the next cell we create the \"jump\" matrix $J$. As you can see, it is a dense matrix!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.0024 & 0.0373 & 0.1934 & 0.3338 & 0.1934 & 0.0373 & 0.0024 & 0.0 & 0.0\\\\0.0 & 0.0024 & 0.0373 & 0.1934 & 0.3338 & 0.1934 & 0.0373 & 0.0024 & 0.0\\\\0.0 & 0.0 & 0.0024 & 0.0373 & 0.1934 & 0.3338 & 0.1934 & 0.0373 & 0.0024\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0.0024  0.0373  0.1934  0.3338  0.1934  0.0373  0.0024   0.0     0.0  ⎤\n",
       "⎢                                                                      ⎥\n",
       "⎢ 0.0    0.0024  0.0373  0.1934  0.3338  0.1934  0.0373  0.0024   0.0  ⎥\n",
       "⎢                                                                      ⎥\n",
       "⎣ 0.0     0.0    0.0024  0.0373  0.1934  0.3338  0.1934  0.0373  0.0024⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "J = np.zeros((Nspace-2, Nspace + 2*extraP))\n",
    "for i in range(Nspace-2):\n",
    "    J[i, i:(len(nu)+i)] = nu\n",
    "display_matrix(J.round(4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have all the ingredients to solve the backward in time algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15.205937181777447\n"
     ]
    }
   ],
   "source": [
    "# Backward iteration\n",
    "for i in range(Ntime-2,-1,-1):\n",
    "    offset[0] = a * V[extraP,i]\n",
    "    offset[-1] = c * V[-1-extraP,i]\n",
    "    V_jump = V[extraP+1 : -extraP-1, i+1] + dt * (J @ V[:,i+1])\n",
    "    V[extraP+1 : -extraP-1, i] = DD.solve( V_jump - offset )    \n",
    "\n",
    "# finds the option at S0\n",
    "oPrice = np.interp(X0, x, V[:,0])\n",
    "print(oPrice)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Is the previous method efficient?\n",
    "\n",
    "Well NO!\n",
    "\n",
    "Since the integral we are considering is a convolution integral, we should take advantage of the [convolution theorem](https://en.wikipedia.org/wiki/Convolution_theorem).\n",
    "\n",
    "We can use two python functions:\n",
    "- [fftconvolve](https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.fftconvolve.html#scipy.signal.fftconvolve) Convolves two arrays using FFT.\n",
    "- [convolve](https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.convolve.html) Convolves two arrays. The user can specify the method. If the length of the array is smaller than 500 it is better to use the definition of convolution, otherwise it is better to use the FFT (and it calls fftconvolve).\n",
    "\n",
    "Let us check that the output is the same:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 3.2055702  22.61411538 80.66390056]\n",
      "[ 3.2055702  22.61411538 80.66390056]\n"
     ]
    }
   ],
   "source": [
    "# example\n",
    "from scipy import signal\n",
    "\n",
    "print(signal.fftconvolve(V[:,-1], nu, mode=\"valid\"))\n",
    "print(J @ V[:,-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15.20593718177744\n"
     ]
    }
   ],
   "source": [
    "# Backward iteration using fftconvolve:\n",
    "for i in range(Ntime-2,-1,-1):\n",
    "    offset[0] = a * V[extraP,i]\n",
    "    offset[-1] = c * V[-1-extraP,i]\n",
    "    V_jump = V[extraP+1 : -extraP-1, i+1] + dt * signal.fftconvolve(V[:,i+1], nu, mode=\"valid\")\n",
    "    V[extraP+1 : -extraP-1, i] = DD.solve( V_jump - offset )    \n",
    "\n",
    "# finds the option at S0\n",
    "oPrice = np.interp(X0, x, V[:,0])\n",
    "print(oPrice)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec3'></a>\n",
    "## Comparison with other numerical methods\n",
    "\n",
    "\n",
    "In the class `Merton_pricer` I made the following choice for the parameters:    \n",
    "```python\n",
    "        S_max = 6*float(self.K)                \n",
    "        S_min = float(self.K)/6\n",
    "```\n",
    "and\n",
    "```python\n",
    "extraP = int(np.floor(5*dev_X/dx))\n",
    "```\n",
    "The reason is that I want the parameters $A_1$, $A_2$, $B_1$, $B_2$ to be as large as possible.\n",
    "\n",
    "In the backward iteration I used the FFT approach:\n",
    "\n",
    "```python\n",
    "V_jump = V[extraP+1 : -extraP-1, i+1] + dt * signal.convolve(V[:,i+1],nu[::-1],mode=\"valid\",method=\"fft\")\n",
    "```\n",
    "\n",
    "The correct code to use is `nu[::-1]`.    \n",
    "This is because our convolution has the form\n",
    "$\\sum_{k = -K_1}^{K_2} \\nu_k V^{n}_{i+k}$, but the convolution in the [numpy.convolve](https://docs.scipy.org/doc/numpy/reference/generated/numpy.convolve.html) function is defined as\n",
    "$\\sum_{k = -K_1}^{K_2} \\nu_k V^{n}_{i-k}$. Therefore it is necessary to invert the vector!    \n",
    "(In the code above, I did not invert `nu` for clarity. The code worked because the considered `nu` was symmetric).\n",
    "\n",
    "Let us compare the solution of the Merton PIDE with other numerical methods: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from functions.Parameters import Option_param\n",
    "from functions.Processes import Diffusion_process, Merton_process\n",
    "from functions.BS_pricer import BS_pricer\n",
    "from functions.Merton_pricer import Merton_pricer "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creates the object with the parameters of the option\n",
    "opt_param = Option_param(S0=100, K=100, T=1, exercise=\"European\", payoff=\"call\" )\n",
    "opt_param_p = Option_param(S0=100, K=100, T=1, exercise=\"European\", payoff=\"put\" )\n",
    "\n",
    "Merton_param = Merton_process(r=0.1, sig=0.2, lam=0.8, muJ=0, sigJ=0.5)\n",
    "Merton = Merton_pricer(opt_param, Merton_param)\n",
    "Merton_p = Merton_pricer(opt_param_p, Merton_param)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**PIDE price:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(22.01403904360017, 40.36621618270874)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Merton.PIDE_price((12000,10000), Time=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Closed formula:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22.016367621905697"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Merton.closed_formula()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Fourier inversion:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22.0163676219057"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Merton.Fourier_inversion()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Monte Carlo** method gives the value: (the output includes the price, the standard error and the execution time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(22.01260319665876, 0.05643812936401397, 64.60239958763123)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Merton.MC(1000000, Err=True, Time=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot of the call:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Merton.plot([50,200,0,100])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot of the put:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Merton_p.plot([40,180,0,80])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### OK cool! It works!\n",
    "\n",
    "But what happens if we select some \"strange\" set of parameters?    \n",
    "Let's try."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PIDEprice:  50.19209080990695\n",
      "Closed formula:  92.84579753439006\n",
      "Monte Carlo price and std error:  (0.021836642589105403, 0.010662297105708677)\n"
     ]
    }
   ],
   "source": [
    "Merton_param = Merton_process(r=0.1, sig=0.1, lam=0.1, muJ=0, sigJ=3.1)\n",
    "Merton = Merton_pricer(opt_param, Merton_param)\n",
    "\n",
    "print( \"PIDEprice: \", Merton.PIDE_price((12000,10000)) )\n",
    "print( \"Closed formula: \", Merton.closed_formula() )\n",
    "print( \"Monte Carlo price and std error: \", Merton.MC(500000, Err=True) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What happened?     \n",
    "Three methods... three different outputs.  This is not good. \n",
    "\n",
    "Do not worry. The model is fine. And the algorithms are fine too.     \n",
    "The last set of parameters is the problem.    \n",
    "To be precise, the model is fine under a certain set of parameters. Let us investigate this feature."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec4'></a>\n",
    "## Model limitations\n",
    "\n",
    "Let us inspect the behavior of the pricing function (Merton closed formula) under different values of `lam` and `sigJ`.     \n",
    "\n",
    "In the plot we can see the curves obtained for different values of `lam`. \n",
    "\n",
    "The model works properly for `sigJ` smaller than a certain level dependent on `lam`.    \n",
    "For `sigJ` too big, the price drops to zero. However, even at the peak of the curve, the three different numerical algorithms can give different outputs.    \n",
    "Under several numerical tests, I found that the model works properly for all values `sigJ` on the left side of the peak of the curve (but not too close to the peak).\n",
    "\n",
    "As you can see, for high values of `sigJ`, the calculations produce overflows and NaNs. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jovyan/work/functions/BS_pricer.py:72: RuntimeWarning: overflow encountered in exp\n",
      "  return S0 * ss.norm.cdf( d1 ) - K * np.exp(-r * T) * ss.norm.cdf( d2 )\n",
      "/home/jovyan/work/functions/BS_pricer.py:72: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  return S0 * ss.norm.cdf( d1 ) - K * np.exp(-r * T) * ss.norm.cdf( d2 )\n",
      "/home/jovyan/work/functions/BS_pricer.py:72: RuntimeWarning: overflow encountered in double_scalars\n",
      "  return S0 * ss.norm.cdf( d1 ) - K * np.exp(-r * T) * ss.norm.cdf( d2 )\n",
      "/home/jovyan/work/functions/Merton_pricer.py:78: RuntimeWarning: overflow encountered in double_scalars\n",
      "  tot += ( np.exp(-lam2*self.T) * (lam2*self.T)**i / factorial(i) ) \\\n",
      "/home/jovyan/work/functions/Merton_pricer.py:78: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  tot += ( np.exp(-lam2*self.T) * (lam2*self.T)**i / factorial(i) ) \\\n"
     ]
    }
   ],
   "source": [
    "sigJs = np.linspace(0.01, 10, 1000)\n",
    "lambdas = [0.00001, 0.0001, 0.001, 0.01, 0.1, 1, 10]\n",
    "Mert_prices = []\n",
    "\n",
    "for j in lambdas:\n",
    "    curve = []\n",
    "    for i in sigJs:\n",
    "        Merton_param = Merton_process(r=0.1, sig=0.2, lam=j, muJ=0, sigJ=i)\n",
    "        Merton = Merton_pricer(opt_param, Merton_param)\n",
    "        curve.append(Merton.closed_formula())\n",
    "    Mert_prices.append(curve)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 2016x4320 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,8))\n",
    "for i,j in enumerate(lambdas):\n",
    "    plt.plot(sigJs, Mert_prices[i], label=\"lam=\"+str(j))\n",
    "plt.plot(sigJs, [BS_pricer.BlackScholes(payoff='call', S0=100., K=100., T=1., r=0.1, sigma=0.2)]*len(sigJs),\n",
    "         label=\"BS price\", color=\"black\" )\n",
    "plt.xlabel(\"sigJ\"); plt.ylabel(\"Mert price\"); plt.title(\"Merton price as function of sigJ\")\n",
    "plt.axis([0,7,0,110])\n",
    "plt.legend()\n",
    "plt.figure(figsize=(28,60))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec5'></a>\n",
    "## Comparison with the Black Scholes PDE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us compare the Merton curve with the Black Scholes curve, for a European call option.    \n",
    "The volatility of the BS model is chosen equal to the standard deviation of the Merton process. \n",
    "\n",
    "Looking at the plot we can see the different shape of the two curves."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "standard deviation:  0.8988882021697694\n",
      "kurtosis:  2.823252622291932\n"
     ]
    }
   ],
   "source": [
    "# Creates the object with the parameters of the option\n",
    "opt_param_c = Option_param(S0=100, K=100, T=1, exercise=\"European\", payoff=\"call\" )\n",
    "\n",
    "# Creates the object with the parameters of the process\n",
    "Merton_param = Merton_process(r=0.1, sig=0.2, lam=1.2, muJ=0, sigJ=0.8)\n",
    "diff_param = Diffusion_process(r=0.1, sig=np.sqrt(Merton_param.var))\n",
    "\n",
    "print(\"standard deviation: \", np.sqrt(Merton_param.var) )\n",
    "print(\"kurtosis: \", Merton_param.kurt)\n",
    "\n",
    "# Creates the object of the pricer: call\n",
    "BS_c = BS_pricer(opt_param_c, diff_param)\n",
    "Merton_c = Merton_pricer(opt_param_c, Merton_param)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Merton closed formula, call:  39.525220975930694\n",
      "BS closed formula, call:  37.987106518471414\n"
     ]
    }
   ],
   "source": [
    "print(\"Merton closed formula, call: \", Merton_c.closed_formula() )\n",
    "print(\"BS closed formula, call: \", BS_c.closed_formula() )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Merton PIDE call: 39.4908331514349\n",
      "BS PDE call: 37.9848259795486\n"
     ]
    }
   ],
   "source": [
    "print(\"Merton PIDE call:\", Merton_c.PIDE_price((13000,10000)))\n",
    "print(\"BS PDE call:\", BS_c.PDE_price((8000,5000)) ) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABAAAAAVCAYAAABPPm7SAAAABHNCSVQICAgIfAhkiAAAAF5JREFUOI1jYKAicGBgYPiPhG8gyYmgyf2HSbBgMeggAwPDAQYGhjdIYt8YGBgaoewEBgYGeXwuaCDg0gPILmAioJggGDVg1IBRAzCBAwOF5cEDBkSeZ2DAXR4MMgAAUJocEs/sZrAAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle \\left[ \\right]$"
      ],
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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x27O8cePG9OrVi5o1a7Jt2zZat27NqlWrAPjwww956qmnGDt2LKdOnaJYsWJUqlQJgLVr17Jt2zYyZ87M8uXLGTBgAHPnzgVg4MCBAPz444/s2rWLKlWqRO9HuWXLFjZv3kyaNGnIlSsXnTt35uGHH46O59KlSwQFBREcHExgYCCnT58mXbp0N/0M586dI1++fPTq1YuIiAgeffRRzp07h7+/P8HBwQQFBXHs2DF69+7N4sWL8ff3p1+/fnzyySf07Nnzlr9bERGRRG/pUmjRAo4cgf794dVXIUUKLl26+ctUIYsjBQoUYP/+/UydOpUaNWpcdW7hwoX07duXgIAAypcvT3h4OL///jsAlStXJnPmzNe95g8//BDdm5Y7d26yZ88enZBVrFiRu+++m7Rp0/LEE0/w22+/XfXa3bt388ADDxAYGAjAXXfdRcqUN8/H/fz8qO/L6FOmTEm1atWYM2cOERERfPfdd9SuXZt169axY8cOSpcuTUBAABMmTPif9xYREUnyLl2CN96ASpUgQwZYtw5efx1SpGDvXihV6uYvT9IVsthUsuLSM888w2uvvcby5cs5fvx49HFrLd988w25cuW66vnr16/H39//hte72b6jadKkif7Zz8+PiIiI/3mtMeZ/XpcyZUqioqKiH4eHh0f/nDZtWvz8/KIfBwUFMXToUDJnzkxgYCAZM2bEWkvlypWZOnXqDWMTERFJ0nbtgqZNYdMmaN8eBg4Ef3+shYkToVMnSJ365pdQhSwOtW7dmp49e5I/f/6rjletWpXPP/88OsHavHnzdV+fMWNGzpw5E/34ySefZPLkyQDs2bOH33///X+SuhvJnTs3YWFhbNy4EYAzZ84QERFBjhw52LJlC1FRURw4cIANGzbc8Brly5dn06ZNjBo1iqCgIABKlCjB6tWr2bdvHwDnz5+PrtqJiIgkadbCiBFQuDD89hvMmgXDh4O/P6dPQ7Nm0LIlFCkCW7fe/FJKyOJQtmzZePnll//n+DvvvMPly5cpUKAA+fLl45133rnu6wsUKEDKlCkpWLAggwYNomPHjkRGRpI/f36CgoIYP378VZWxm0mdOjXBwcF07tyZggULUrlyZcLDwyldujQ5c+Ykf/78vPbaaxQuXPiG1/Dz86NmzZrMnz8/eoRHlixZGD9+PE2aNKFAgQKUKFGCXbt2xSomERGRROvYMahbFzp0gDJl4McfoXZtANavdz3nwcHwwQeurSxGW/d1mZstgyV0RYsWtSEhIVcd27lzJ3ny5PEoIrkZ/W5ERCRJWLgQnnvO3U3Zty+8/DKkSEFUlOvjf+cdePBBmDLFjSC7whgTaq0ter1LqkImIiIiEhvh4fDKK1C1KmTODBs2QNeukCIFYWFQuTK8+aYrnG3denUy9k+SdFO/iIiIyB3x00/w7LNuptiLL7pSmG981Ny5rlfswgUYPRpat4br3Ed3U6qQiYiIiNyItTBkCBQtCn/+6bKvzz+HdOkID4eXXoJatVyPWGiomwV7q8kYqEImIiIicn2HD7ty17x5UL06jBsHWbMCsHMnNG7sCmZdurhWsljeZ3ddqpCJiIiIXGvePChQAJYscRWx776DrFmxFkaNcqMswsJcwWzQoH+XjIESMhEREZG/XbgAnTvD00+7alhIiOsZM4aTJ6FRI3j+edewv22be9qdoIQsDvj5+REQEEC+fPlo2LAh58+fv6PXHzx4MHny5KFp06ZcvHiRSpUqERAQQHBw8B19HxERkWRl2zYIDHQ9Y126uLso8+UDYPVqN1ts1izo1w++/x4eeODOvbUSsjiQLl06tmzZwvbt20mdOjXDhw+/o9cfNmwY8+bNY/LkyWzevJnLly+zZcuW6On5IiIicguiotx+i4GBcPw4LFjg1iHTpiUyEnr1giefhFSpXGL2xhuQ4g5nUErI4ljZsmWjtxWqU6cORYoUIW/evIwcORKAMWPG0LVr1+jnjxo1ildeeQWATz75hHz58pEvXz4+9W3M2aFDB3755ReeeeYZ+vXrR7NmzdiyZQsBAQH8/PPP8fzpREREErlDh1zDfteuUK2aq5JVrQrAgQPw1FPw7rtu4sWmTVCsWNyEkaTvsuzSpQtbtmy5o9cMCAiITo7+SUREBPPnz6datWoAjB07lsyZM3PhwgUCAwOpX78+jRs3pkCBAvTv359UqVIxbtw4RowYQWhoKOPGjWP9+vVYaylevDjlypVj+PDhLFiwgGXLlvGf//yH4sWLM2DAAObOnXtHP6eIiEiSN3u2m1Nx7hx88YXbGNw3s2LGDGjbFi5fdhuEN28et6GoQhYHLly4QEBAAEWLFuWRRx6hTZs2gOv9KliwICVKlODAgQPs3bsXf39/nnrqKebOncuuXbu4fPky+fPn54cffqBu3br4+/uTIUMG6tWrx6pVqzz+ZCIiIknA+fPwwgtu78ls2dwAsQ4dwBjOn3c/1q8P//0vbN4c98kYJPEKWWwrWXfalR6ymJYvX87ixYtZu3Yt6dOnp3z58oSHhwPQtm1b+vTpQ+7cuWnVqhUAiXmPURERkQRr0yZo2hR27YLXXoPevaNnVvz4o5sttmOH6xP74ANInTp+wlKFLJ789ddfZMqUifTp07Nr1y7WrVsXfa548eIcOHCAKVOm0KRJEwCefPJJZs2axfnz5zl37hwzZ86kbNmyXoUvIiKSuEVGuumtxYvD6dOwaBF8/DGkSYO1MHSo6+k/ccLtHd6vX/wlY5DEK2QJSbVq1Rg+fDgFChQgV65clChR4qrzjRo1YsuWLWTKlAmAwoUL07JlS4r5ugfbtm1LoUKF4j1uERGRRO+336BFC1i5Eho0gBEj3ObgwLFjrlfs22+hRg03jP++++I/RJOYl8aKFi1qQ0JCrjq2c+dO8uTJ41FEt69mzZp07dqVihUreh1KnEmsvxsREUnEJk+Gjh3/3pOyefPoxv3Fi12edvy4q4i9/PLt7UMZW8aYUGtt0eud05Klx06dOsXjjz9OunTpknQyJiIiEq9OnnSzKpo1c8Ndt2512ZcxXLrkesQqV4Z77nHzX7t0idtk7J9oydJj99xzD3v27PE6DBERkaRj+XKXfIWFuc787t0hpUt5du/+e6bYCy/AgAGQPr234UISrZAl5mXYpEq/ExERiXMXL7rS11NPQdq0sGYN9OgBKVNiLYweDYULu5ayWbNg2LCEkYxBEkzI0qZNy/Hjx5UAJCDWWo4fP07atGm9DkVERJKqHTugRAl352S7dm6AmO/GuBMnoGFDd7hkSTeMv3Ztj+O9RpJbssyWLRsHDx7k6NGjXociMaRNm5Zs2bJ5HYaIiCQ1V5r133gDMmRwt0s+80z06eXLXR//4cPQvz+8+uqd34fyTkhyCVmqVKnImTOn12GIiIhIXDt0CFq3dpuB16gBY8bA/fcDbsuj996Djz6Cxx6DtWuhSBFvw72ZJJeQiYiISDIwa5YbIHbunJvq+sIL0bdJ7tvnhvFv2OCe8umn4O/vcbz/IAEW7URERERu4OxZ1wxWty5kz+5ul+zYEYzBWpgwAQoVgr17Yfp0GDUq4SdjoIRMREREEov16122NWaMG2Wxdi34Bo6fOuXGWbRs6ZYmt251G4QnFkrIREREJGGLiIBevaB0abh0yXXqf/RR9GaTP/wAAQEwbRp8+CEsWQIPP+xtyLdKPWQiIiKScP38s7tNcu1a1xg2ZIgbr4/L0z74AHr3hhw5YPVqt3d4YqSETERERBIea2H8eHjpJfDzgylToEmT6NO//urys7Vr4bnn4PPPIWNG78L9t+JsydIYM9YYc8QYsz3GsczGmEXGmL2+vzPFOPemMWafMWa3MaZqXMUlIiIiCdzx49CggRtpUaSIm+QaIxmbMsUtUf70E0yd6vK2xJyMQdz2kI0Hql1zrDuwxFr7GLDE9xhjzBNAYyCv7zXDjDF+cRibiIiIJEQLF0L+/DBnDvTr5xrCHnkEgNOn3epl06buKVu3QuPGHsd7h8RZQmatXQmcuOZwbWCC7+cJQJ0Yx7+y1l601v4K7AOKxVVsIiIiksCEh0OXLlC1qusRW7/eTd/3c/WZdetcVWzqVHj/fdfXnyOHpxHfUfF9l2VWa+0hAN/f9/mOPwQciPG8g75j/8MY87wxJsQYE6LtkURERJKAbdugaFH47DPo3BlCQ914CyAy0jXtlynj2spWroSePSFlEuuCTyhjL8x1jl13d3Br7UhrbVFrbdEsWbLEcVgiIiISZ6Ki4JNPIDDQ9Y3NmweDB0O6dAD8/jtUqADvvANBQbBlC5Qq5XHMcSS+88vDxpgHrLWHjDEPAEd8xw8CMSeGZAPC4jk2ERERiS8HD7rbI5cuhdq13Uj9GIWWr7+G9u1dhWzSJGjWzMNY40F8V8hmA8/5fn4O+DbG8cbGmDTGmJzAY8CGeI5NRERE4sPXX7uu/HXrXCI2c2Z0MnbmjLu5MigIcuVyVbGknoxB3I69mAqsBXIZYw4aY9oAfYHKxpi9QGXfY6y1PwFfAzuABUAna21kXMUmIiIiHjh9Glq0cNnW44+7bKtt2+hNwdeudY37EybA22/DqlXw6KMexxxP4mzJ0lrb5AanKt7g+R8CH8ZVPCIiIuKhlStdMnbggOvK79EDUqUC3MT93r3dn2zZYMUK18SfnCSxexREREQkQbl40SVgH3/syl0//AAlS0af/vlntyS5bp37e8gQuPtuD+P1iBIyERERiRs//uiyrG3b4PnnYeBAyJABcCMsJkxwUy78/Nx8saQy5PV2JJSxFyIiIpJUXBlnUbQo/Pmnm7o/YkR0MnbiBDRqBK1a/b0zUnJOxkAVMhEREbmTfv8dWraEZcuuO85i8WI37eLoUbcz0quvRg/jT9ZUIRMREZF/z1r48ks3zmLjRhgz5qpxFhcvuuSrcmW46y7XMxZjZ6RkTxUyERER+XdOnIAOHWDaNChdGiZOvGpexU8/wbPPuqXJjh1df3/69B7GmwCpQiYiIiK3b+FCVxWbORP69HEzK3zJmLVuJ6QiRVwr2dy5MHSokrHrUUImIiIit+78eXeLZNWqbk7Fhg3w5pvRa5CHDkH16vDyy1CpkquOPf20xzEnYErIRERE5NaEhrqy15AhLuMKDYVChaJPf/stFCjgZsEOG+Zussya1cN4EwElZCIiIhI7V0bqlyjhNp1ctAg+/RTSpQPg3Dk3bqxOHXj4YZenvfBC9M5IchNq6hcREZF/tm+f2/po7Vpo0sQ1g2XKFH1640Zo2tQ9rVs36NULUqf2MN5ERhUyERERuTFr3SyxgADYuROmTHF/fMlYZCR8+CGUKgUXLsDSpdC3r5KxW6UKmYiIiFzf4cPQtq27PbJiRRg3zq1F+uzfD82bu+0pg4Lgiy+uKprJLVCFTERERP7Xt9+6cRZX+sQWLoxOxq7MgC1YELZudWPHpk5VMvZvKCETERGRv50546piderAQw/Bpk3uTsoULmU4dcoNeW3e3OVrW7e6n9W4/+8oIRMRERFn9WrXKzZunJsptn49PPFE9Only904i2nT4IMP3OOcOT2LNklRQiYiIpLcXboEb78NTz7p1iNXrHBT932d+eHh8Npr8NRTkDYtrFkDPXpASnWi3zH6KkVERJKzHTugWTPYvBlat3b9YhkzRp/eutWd3r7dzRT7+GPw9/cw3iRKFTIREZHkKCrq740mDxxwe1GOGROdjEVGuuSrWDE4dgzmzXNT95WMxQ1VyERERJKbgwehVStYvBhq1oTRo6/a22j/fnjuObf1Ub16MGIE/Oc/3oWbHKhCJiIikpx89ZW7PXLtWhg5EmbPjk7GrIUJE1zj/ubNMH48TJ+uZCw+KCETERFJDk6ccFseNWkCuXPDli3Qrl30vIpjx6BhQ2jZ0t1ouW2bq5JpnEX8UEImIiKS1C1YAPnyuXJX796wahX83/9Fn54/3xXNZs+G/v1h2TLIkcO7cJMjJWQiIiJJ1dmz7tbI6tUhc2bYsMGNt/DNqzh3Djp2hBo13LLkxo3w+uvg5+dx3MmQEjIREZGkaM0at/Y4YoQbIhYSAoUKRZ/esAEKF4bhw+HVV10yVrCgh/EmcadPn77peSVkIiIiScnFi3aiFroAACAASURBVG7KftmybnbF8uVufkXatABcvgzvvw+lSsGFC7BkCQwYEH1a4sCuXbsoVqzYTZ+jhExERCSp2LbNDQ7r29cNed22zU3f99mzB8qUgffec73927ZBhQrehZscfPvttxQrVowTJ07c9HlKyERERBK7yEjo1w+KFoXDh2HOHBg1KnrIq7VuabJQIdi7F4KDYdIkuOcej+NOwqKioujZsyd16tQhV65chIaG3vT5GgwrIiKSmP38s5tPsXo11K/vMq8Yg8MOHYI2bdydlFWqwNix8NBDHsabDJw6dYqmTZsyb948WrVqxbBhw0j7D2vCqpCJiIgkRta6hv2CBd1Gk19+CdOmXZWMzZjhxlksWwZDhrjpF0rG4tb27dsJDAxk4cKFDBs2jDFjxvxjMgZKyERERBKfsDA3q6JDByhZEn78EZo2jZ7ievq02xmpfn03T2zzZujUSUNe49r06dMpUaIEZ8+eZdmyZbzwwguYWH7pSshEREQSk+BgN+R1xQpX9vr+e3j44ejTK1e6rY8mToR33nE7JOXO7WG8yUBkZCTdu3enYcOGFChQgNDQUMqUKXNL11BCJiIikhhc2fqocWN4/HG39VGnTpDC/VMeHu7miZUv7+a+/vAD9OoFqVJ5G3ZSd/z4cWrUqEG/fv1o3749y5Yt48EHH7zl66ipX0REJKFbsMCNsTh61G191K1b9LR9cDNfW7SAnTvdYP7+/SFDBg/jTSa2bt1K3bp1+eOPPxg1ahRt27a97WupQiYiIpJQnTt3062PLl92M8VKlHB9Y99/D8OGKRmLD1OmTKFkyZJcunSJlStX/qtkDJSQiYiIJExr1rg7KG+w9dGOHa6f//333Urmjz+6sRYStyIiInj11Vdp2rQpRYsWJTQ0lOLFi//r6yohExERSUguXoS33rrh1kdRUfDJJ24fyv37Yfp0N+Q1UyZPo04Wjh49SpUqVfjkk0/o3LkzS5YsIWvWrHfk2uohExERSSi2bYPmzd3fbdu6zMs3bR/g11+hZUt3J+Uzz8DIkXCH8gH5B6GhodStW5cjR44wfvx4nnvuuTt6fVXIREREvBYZ6TrxAwNvuPXR6NFunMXmzTBuHMyapWQsvkyYMIHSpUtjjGH16tV3PBkDJWQiIiLe+vlnKFfO3TlZq5abul+zZvTpQ4fc4XbtXL7244+uSqYhr3Hv8uXLdO7cmZYtW1KqVClCQkIoUqRInLyXEjIREREvWOvWHG+y9dGVGbBLlsBnn8HixZA9u4cxJyN//vknFStWZMiQIbz66qssXLiQLFmyxNn7qYdMREQkvoWFuR6x+fOhUiW343eMafvHj7uZr8HBUKwYTJigafvxad26ddSvX5+TJ08yZcoUmjRpEufvqQqZiIhIfLEWpkxxZa/ly+Hzz/9n66N589zpb76BDz6A1auVjMWn0aNHU65cOdKkScPatWvjJRkDJWQiIiLx48gRaNDAbQKeOzds3Qovvhi99dGZM/D88/D0027VcsMG6NHjqoH8EocuXrxI+/btadeuHeXLlyckJISCBQvG2/srIRMREYlrM2a4stfcudCvH6xaBY89Fn165UrXSjZ6NLzxxv/MgJU4FhYWRvny5Rk5ciTdu3dn3rx5ZM6cOV5jUN4tIiISV06ehM6dYfJkN8l12TLImzf6dHi42wlp0CDImdMlZmXKeBhvMvTDDz/QoEEDzp49y7Rp02jQoIEncahCJiIiEhfmz3dVseBgt+HkunVXJWMhIVCkiJv92r69W8FUMhZ/rLUMGzaMChUqkDFjRtavX+9ZMgZKyERERO6s06fd0LAaNdx+RuvXw7vvQqpUgNsZqUcPtyH4qVMub/viC20IHp/Cw8Np06YNnTp1okqVKmzcuJG8MZJlLyghExERuVOWLXPj9MeOhe7dITTULVX6bN7shrt++CE0awY//QTVqnkYbzJ04MABypYty7hx4+jZsydz5szhnnvu8Tos9ZCJiIj8a+fPw5tvwuDBrln/hx+gZMno05cvQ58+0Lu3u4Ny9mw3fV/i1/Lly2nUqBHh4eHMmjWL2rVrex1SNFXIRERE/o21ayEgwCVjL70EW7ZclYxt2+aGu773HgQFuaqYkrH4Za3l008/pVKlStx7771s2LAhQSVjoIRMRETk9ly86JYly5SBS5dg6VK3v1H69ABERLilyaJF3WD+GTPc7kjxPE0h2Tt//jzNmzena9eu1KpVi/Xr15M7AU7a1ZKliIjIrdq0CVq0cOWudu1g4EDImDH69E8/uQ3AQ0JcVWzIkKu2qJR4sn//furWrcvWrVv54IMPeOutt0iRImHWopSQiYiIxFbMZrD77nP7HFWvHn06IsLlZj17wl13wddfQ8OGHsabjC1atIjGjRsTGRnJ3LlzqVGjhtch3ZQnaaIxpqsx5idjzHZjzFRjTFpjTGZjzCJjzF7f35m8iE1EROS6fvrJzap47z1o3Bi2b78qGdu1y61edu8ONWu6pysZi3/WWvr370+1atV48MEHCQkJSfDJGHiQkBljHgJeAopaa/MBfkBjoDuwxFr7GLDE91hERMRbkZHQv78bX3HggGsGmzTJzRjznR440PX1790LU6fC9OmugCbx69y5czRu3Jhu3bpRv3591q5dy//93/95HVaseLWQmhJIZ4xJCaQHwoDawATf+QlAHY9iExERcfbuhbJloVu3v8tedetedfrJJ+G116BqVXe6cWMwxsOYk6l9+/ZRokQJpk+fTr9+/QgODiZDIpq2G+8JmbX2D2AA8DtwCPjLWrsQyGqtPeR7ziHguv/fwhjzvDEmxBgTcvTo0fgKW0REkpOoKPj8c7fj986dbi/K6dMhS5bo05995k7v2OEKZrNmwf33exx3MjV//nwCAwMJCwtjwYIFvPHGG5hElhV7sWSZCVcNywk8CPgbY5rF9vXW2pHW2qLW2qJZfP/FEBERuWN++w0qVXIzxSpUcGWvZ5+NLnv9/LM73KXL36ebNVNVzAtRUVF8+OGHPP3002TPnp2QkBAqV67sdVi3xYsly0rAr9bao9bay8AMoBRw2BjzAIDv7yMexCYiIsmVtTB6NOTP7+ZVjB4Nc+fCgw8Crio2dKjbGWnLFhg37qrTEs9Onz5N/fr16dGjB88++yxr1qwhZ86cXod127xIyH4HShhj0htXT6wI7ARmA8/5nvMc8K0HsYmISHIUFuZ6xNq1c5Ncf/wR2rSJLnv98osrmr34omsp277dzRlTVcwbu3fvpnjx4syZM4dBgwYxadIk0vsG8iZW8T6HzFq73hgzHdgERACbgZFABuBrY0wbXNKmm4VFRCRuWQsTJ7r1x4sXXd9Yx47gGx56pSrWvTv4+cHIkdC2rRIxL82ePZvmzZuTOnVqFi1aRIUKFbwO6Y7wZDCstfZd4N1rDl/EVctERETiXlgYtG/v1h3LlHFrkDFGJOzdC61bu33Cq1VzydjDD3sYbzIXFRXF+++/T69evShSpAgzZszgkUce8TqsOyZh7h8gIiISV6x1t0XmzQtLlsCgQbBiRXQydmWuWIECbmly3Dg3kF/JmHdOnTpF7dq16dWrFy1btmTVqlVJKhkDbZ0kIiLJyaFD0KEDzJ4NpUu7bOuxx6JP79jhqmLr18Mzz8AXX6hp32s7duygTp06/PrrrwwdOpQXXngh0Y20iA1VyEREJOmz1s0Sy5sXFi50JbAVK6KTsYgI+OgjKFTILVVOnuzmiikZ89Y333xD8eLFOX36NEuXLqVjx45JMhkDJWQiIpLU/fkn1KvnhoXlzu1mVrzyiuvSB7Ztc1tUvvWWq4rt2HHV2DHxQGRkJG+99RYNGjQgb968hIaGUrZsWa/DilNKyEREJGmy1m0smTcvzJ8PH38Mq1ZBrlwAXLoE77/vplz8/jtMm+b+ZM3qcdzJ3IkTJ3j66af56KOPeP7551mxYgUPPfSQ12HFOfWQiYhI0nP4MLzwAsycCcWLw/jxrjrms2kTtGrlqmPPPuu2QfrPf7wLV5ytW7dSt25d/vjjD0aOHEm7du28DineqEImIiJJh7UQHOyqYvPmQb9+sHp1dDJ28SL06AHFisHRo/Dtt65fTMmY97766itKlizJxYsXWbFiRbJKxkAJmYiIJBVHjkDDhtC4Mfz3v7B5M7zxRnSv2IYNULgwfPghNG/u9qB85hmPYxYiIiJ47bXXaNKkCUWKFCE0NJQSJUp4HVa8U0ImIiKJ39dfu6rYnDnQt6+riuXJA8CFCy4vK1kSTp92hbNx4yBTJo9jFo4dO0bVqlUZOHAgnTp1YsmSJdx///1eh+UJ9ZCJiEjidfQodOrkuvGLFnW9YnnzRp9evdrNFduzB55/Hvr3h7vv9i5c+dumTZuoW7cuhw8fZty4cbRs2dLrkDylCpmIiCRO06e75GvWLOjTB9aujU7Gzp6Fl15yG4FfugSLF8OIEUrGEopJkyZRunRprLX88MMPyT4ZAyVkIiKS2Bw7BkFBrl/skUfcLZNvvgkp3aLPggUuLxsyBF58EX78ESpqp+QE4fLly7z88su0aNGCEiVKEBISQtGiRb0OK0FQQiYiIonHjBku25o5E3r3dlWxfPkAOH4cWrSA6tXB399tCj54MGTI4HHMAsDhw4epVKkSgwcPpmvXrixatIj77rvP67ASDPWQiYhIwnf8uCt3ffWVu1Vy8WLInx/4e9LFSy/ByZPwzjvw9tuQJo3HMUu0DRs2UK9ePU6cOMHkyZN59tlnvQ4pwVGFTEREEraZM+GJJ+Cbb6BXL1i3LjoZO3jQja5o0gRy5HCrl716KRlLSMaMGUPZsmVJlSoVa9asUTJ2A0rIREQkYTp+HJo2dftQPvgghIS48leqVERFwfDhLk9bsgQ++cStXvryNEkALl26xAsvvEDbtm0pV64cISEhBAQEeB1WgqWETEREEp5vvnHZ1tdfw3vvuamuBQoAboRFhQpuZ6RixWD7dujaNXr+qyQAYWFhVKhQgeHDh9OtWzfmz5/Pvffe63VYCZp6yEREJOE4csT1ik2bBoUKwcKFULAgAJcvw4ABbkPwdOlg7Fho2RKM8TZkudrq1atp0KABZ86cITg4mEaNGnkdUqKgCpmIiHjPWtewnzev22Cyd29Yvz46Gdu0yVXD3noLatWCnTvd5uBKxhIOay1ffPEFFSpUwN/fn3Xr1ikZuwVKyERExFuHDkHduq4z/9FHXfb19tuQKhUXLkC3bi4Z+/NPN/Vi2jRIprvrJFjh4eG0bduWjh07UqlSJTZu3Eg+3zgSiR0lZCIi4g1rYeJEVxVbsMDta7R6dfS0/eXLXdtY//6uGrZzp8vbJGE5cOAATz75JGPHjqVHjx7MmTOHTNoo9Japh0xEROLfwYPQvr3b6bt0aRgzBnLlAuDUKbcZ+KhRrmC2ZAk89ZTH8cp1rVixgoYNGxIeHs7MmTOpU6eO1yElWqqQiYhI/LEWRo92VbDly+Gzz2DFCsiVC2v/HsQ/Zgy89prb9kjJWMJjrWXw4MFUrFiRzJkzs379eiVj/5IqZCIiEj/274d27dyU/fLlXWL23/8CrmD24ouun79gQfe3tjhMmC5cuED79u2ZNGkStWvXZuLEidx1111eh5XoqUImIiJxKyoKhg1zU1vXrYMvvnDrkP/9L5GR8PnnkCePm3DRvz9s3KhkLKHav38/pUuX5ssvv6RXr17MmDFDydgdogqZiIjEnZ9/hrZt3fJk5cquMSx7dgC2bXMFsw0boGpVl6flzOltuHJjS5YsISgoiIiICObMmcPTTz/tdUhJiipkIiJy50VGwqefuqrY5s2uKez77yF7ds6fh+7d3R7hv/4KU6bA/PlKxhIqay0DBgygSpUqZM2alY0bNyoZiwOqkImIyJ21eze0bg1r1sDTT8OIEfDQQ4BbluzQwSVibdq4JcrMmT2OV27o3LlztGnThuDgYBo0aMC4cePIkCGD12ElSaqQiYjInRER4TKsggXd0LCJE2HOHHjoIY4ehebN3dJkqlSwbJnr6VcylnD9/PPPlCxZkq+//pq+ffvy9ddfKxmLQ6qQiYjIv/fTT25668aNbnrrsGFw//1YC+PHuREWZ85Az57w5puQNq3XAcvNLFiwgCZNmmCMYf78+VStWtXrkJI8VchEROT2Xb7s9p0sVMitQ371FXzzDdx/P3v2QMWKbvUyTx7YssVtDK5kLOGy1tKnTx9q1KjBI488QkhIiJKxeKIKmYiI3J6tW11VbPNmCApy8yuyZOHSJbdy2bu3S75GjHA3WqZQCSBBO3PmDC1btmTGjBk0adKEUaNG4e/v73VYyYYSMhERuTUXL0KfPu7Pvfe68fq+TSbXrHGjLHbsgEaN3I2WDzzgcbzyj/bs2UOdOnXYs2cPn3zyCV26dMEY43VYyYoSMhERib1169ztkTt2uC79Tz+FzJk5dcr1hg0fDg8/7Hr5a9b0OliJjblz59K0aVNSp07NwoULeUp7VXlCBWQREfln585B165QqpTrzp83DyZOxGbKzJQpkDs3jBwJXbq4XE3JWMIXFRXF+++/T61atfi///s/QkJClIx5SBUyERG5ucWL4fnnXdN+p07w0UeQMSN79kDHjm4XpMBAl6MVLux1sBIbf/31F82bN2fOnDm0aNGC4cOHky5dOq/DStZUIRMRkes7edItT1au7IaHrVwJQ4YQnioj773nhvBv3AhDh8LatUrGEosdO3ZQrFgx5s+fz+eff8748eOVjCUAqpCJiMj/mjnTlb+OHnXNYT17Qtq0LFrkDu/bB88+CwMHwv33ex2sxNaMGTN47rnnSJ8+PUuXLqVs2bJehyQ+qpCJiMjf/vwTGjaEevVcprVhA/Tpw5+n0vLss1ClChgDixbB5MlKxhKLyMhI3n77berXr88TTzxBaGiokrEERgmZiIiAtTBhAjzxhLtFsk8f2LCByIKFGToUcuVy817few+2bYNKlbwOWGLr5MmT1KxZkz59+tC2bVtWrlxJtmzZvA5LrqElSxGR5G7/fmjf3u38Xbq022Qyd242bXKHQ0JcAjZ0KDz+uNfByq3Ytm0bdevW5cCBA4wYMYLnn3/e65DkBlQhExFJrqKi3HT9fPncRNchQ2DlSk4/mJuXX3Z3Th44AFOmuFxNyVjiEhwcTMmSJblw4QIrVqxQMpbAKSETEUmOdu2CJ5+El16CsmVh+3Zsx05M+yYFuXO7PK1DB/e0Jk1c35gkDhEREbzxxhs0btyYgIAAQkNDKVmypNdhyT9QQiYikpxcvuz6wwoWhJ07YeJEmDePnyOyU6OG2+7o/vvdQP6hQ+Gee7wOWG7FsWPHqFatGh9//DEdO3Zk2bJlPKC9qxIF9ZCJiCQXmzZB69ZuU/BGjWDwYC7ek5WPP4QPP3Sjxj791M1+Tal/HRKdzZs3U7duXf7880/Gjh1Lq1atvA5JboEqZCIiSd2FC9C9OxQrBkeOuBljwcF8vyUr+fLBO++4rY527oSXX1Yylhh9+eWXlCpVisjISFatWqVkLBFSQiYikpStXOmWJ/v1g1atYMcOfi9ch/r1oVo1SJECvv8epk2Dhx7yOli5VZcvX6ZLly40b96c4sWLExoaSmBgoNdhyW1QQiYikhSdPu1G6pcrB5GRsHgxF4eM4qMv7iFPHpg/37WSbdvmhr1K4nPkyBEqV67MZ599xssvv8yiRYu47777vA5LblOsC9PGmOzAY9baxcaYdEBKa+2ZuAtNRERuy9y58MILEBYGr7wCvXqxaI0/LxaAPXugbl0YNAiyZ/c6ULldGzdupF69ehw7doxJkybRrFkzr0OSfylWFTJjTDtgOjDCdygbMCuughIRkdtw+DAEBUGtWnD33bBmDQe7DqRRK3+qVHGFsnnzYMYMJWOJ2dixYylbtix+fn6sWbNGyVgSEdsly05AaeA0gLV2L6C6qIhIQmAtjB0LefLArFnwwQdcWreJ/iuKkzu32wnpgw9g+3aoXt3rYOV2Xbp0iY4dO9KmTRvKlClDSEgIhQoV8josuUNiu2R50Vp7yfgmAxpjUgI2zqISEZHY2bvX7W+0bJkb9DpyJEsO5uLFQDfUtXZttzyZM6fXgcq/cejQIRo2bMjq1at5/fXX6dOnDyl1O2ySEtvf5gpjzFtAOmNMZaAjMCfuwhIRkZu6fBkGDIBevSBNGhg5kj+qteHV11MQHAyPPupayZ5+2utA5d9au3Yt9evX56+//uKrr74iKCjI65AkDsR2ybI7cBT4EWgPzAN6xFVQIiJyExs3QtGi8NZb8PTTXN62kwF/tSP3EymYNQveew9++knJWGJnrWXEiBGUK1eOdOnSsW7dOiVjSVhsK2TpgLHW2lEAxhg/37Hzt/Omxph7gNFAPtzSZ2tgNxAM5AD2A42stSdv5/oiIknS2bNuiuvgwW5/o1mzWH53bTpVhx07XAI2eLCrjknidvHiRV588UVGjx5N9erVmTx5MpkyZfI6LIlDsa2QLcElYFekAxb/i/f9DFhgrc0NFAR24qpwS6y1j/ner/u/uL6ISNIyfz7ky+f2NmrfngMLd9Lkq9pUqADnz8Ps2W6JUslY4nfw4EHKlSvH6NGjefvtt5kzZ46SsWQgthWytNbas1ceWGvPGmPS384bGmPuAp4EWvqudQm4ZIypDZT3PW0CsBzodjvvISKSZBw9Cl26wJQpkCcP4UtWM3BtKfoUg6go6NkTunWD9Lf1v8iS0KxcuZKGDRty/vx5vvnmG+rVq+d1SBJPYpuQnTPGFLbWbgIwxhQBLtzmez6K60cbZ4wpCIQCLwNZrbWHAKy1h4wxGqshIsmXtTBxohvseuYM9t33mJP/Lbq2S8Uvv0C9ejBwIOTI4XWgcidYaxkyZAivvPIKjz76KMuWLeOJJ57wOiyJR7FdsuwCTDPGrDLGrML1er14m++ZEigMfGGtLQSc4xaWJ40xzxtjQowxIUePHr3NEEREErBffnH7GbVsCblzs3vmDmqsf5faDVKRJg0sWgTffKNkLKm4cOECLVu25KWXXqJ69eps2LBByVgyFKsKmbV2ozEmN5ALMMAua+3l23zPg8BBa+163+PpuITssDHmAV917AHgyA1iGQmMBChatKhmoYlI0hER4YaGvfsupEzJ6YGj+CCsDZ/WMaRP70516gSpUnkdqNwpv/32G/Xq1WPTpk28//779OjRgxQptM10cnTThMwY85S1dqkx5tpF7MeMMVhrZ9zqG1pr/zTGHDDG5LLW7gYqAjt8f54D+vr+/vZWry0ikmht2gRt28LmzUQ9U4cvnxpDt76Z+fNPaN3abQSeNavXQcqdtHTpUoKCgrh06RKzZ8+mVq1aXockHvqnClk5YClwvf+UWOCWEzKfzsBkY0xq4BegFW759GtjTBvgd6DhbV5bRCTxOH/eVcQGDYIsWQjtt5jOs55ibRdDsWLw7bdQrJjXQcqdZK1l0KBBvP766+TKlYtZs2bx+OOPex2WeOymCZm19l1jTApgvrX26zv1ptbaLUDR65yqeKfeQ0QkwVu0yG179OuvHG3+Cm+n6MPo7mnIkgXGjYMWLUCrV0nLuXPnaNu2LV999RX16tVj/PjxZMyY0euwJAH4x/+qW2ujuP0GfhERudbRoy7bqlKFiJRpGdx5L4/NHsi4yWno2hX27HH9/ErGkpZffvmFUqVKERwcTJ8+fZg+fbqSMYkW27EXi4wxr+Hurjx35aC19kScRCUikhRZC+PHw2uvwZkzLG06hpc2t+Snz1NQuTJ89hnkyeN1kBIXFi5cSOPGjbHWMm/ePKpVq+Z1SJLAxPb/f7XGbSi+AgiJ8UdERGJj1y6oUAFat+bXRyvSoPwxKk5uzbnzKZg5E77/XslYUmStpW/fvlSrVo1s2bIREhKiZEyuK7YVsidwCVkZXDP/KmB4XAUlIpJkhIdD377w0UecSXcfH1XfzCdLC+LnZ+jVyxXL0qX758tI4nPmzBlat27N9OnTady4MaNHj8bf39/rsCSBim1CNgE4DQz2PW7iO9YoLoISEUkSli2DDh2I2rOXCSWG89Yvbfhzvh/Nm8NHH8FDD3kdoMSVvXv3UqdOHXbt2sWAAQN45ZVXMMZ4HZYkYLFNyHJZawvGeLzMGLM1LgISEUn0jh2D11+H8eNZ9WAQXf5vI5vW3UXJkvDtHI2xSOq+++47mjZtSsqUKVm4cCEVK2qAgPyz2PaQbTbGlLjywBhTHFgdNyGJiCRS1sKECZA7N/snrSIoz1aeDPuKI+F3MXkyrF6tZCwpi4qKolevXtSqVYtHH32UkJAQJWMSa7GtkBUHWhhjfvc9fgTYaYz5EbDW2gJxEp2ISGKxZw906MDZZRvom20IA860IMX+FLz3niuWpU/vdYASl/766y9atGjB7Nmzad68OSNGjCCdmgPlFsQ2IdMtISIi13PxIvTrR1TvPkxK2Yo3757DoYP+NG3q+sQeftjrACWu7dy5k7p167Jv3z4GDx7Miy++qH4xuWWx3Vz8t7gOREQk0Vm5Etq3Z/WuzHTJ/BMhJ/5Lsfww4zMoUeKfXy6J36xZs2jevDnp06dnyZIllCtXzuuQJJHSHGgRkVt14gS0bcvv5ZrR5EB/yrCaQ+n+y6RJsHatkrHkIDIyknfeeYe6deuSJ08eQkNDlYzJv6KETEQktqyFL7/kXK7C9Bybg1wpf2ZWZE169oTdu6FZM213lBycPHmSWrVq0bt3b1q3bs3KlSvJli2b12FJIhfbHjIRkeRt3z6iOnRk4pIHeTvVRsJsFpo0dDNfH3nE6+Akvmzfvp06derw+++/88UXX9C+fXv1i8kdoYRMRORmLl2Cjz9m6fureDVyAFsoQLFClq8/gdKlvQ5O4tO0adNo1aoVGTNmZPny5ZQqVcrrkCQJUXFdRORGVq5k5xP1qdWjABUvL+Dkwtm47AAAIABJREFUg08wdSqsW2eUjCUjkZGRdOvWjUaNGlGgQAFCQ0OVjMn/t3fnYTaX/x/Hn3fWkMpXG99SopTShrJkSbIkmQVjb+x7+UZSQsqSyJKd7MvQWIusIWSbiUKRLZR9yW7GzNy/P+7xS0VZZuZzzpzX47q6ZubMzDnv675M85p7ed9JTjNkIiJ/dfgwh1p2pcvURxjODDJnsnzUGVq3TkvGjF4XJynp6NGj1KhRg4ULF9K0aVP69+9P+vTpvS5LUiEFMhGRixISODd4NP3f+pXu57px1mSmaeMEOn+Qjjvu8Lo4SWkbNmwgKCiIffv2MXLkSBo0aOB1SZKKKZCJiAAJ679ncrUZvLM9nD3k4pXSp+g1OA358qXxujTxwMSJE2nUqBHZsmVj+fLlFNadV5LMtIdMRALbqVMsr/Ypzz0dS+3tXfhPrix8vdgy++tbyJfP6+IkpcXFxdGmTRtq165NoUKFiI6OVhiTFKEZMhEJTNaybdAC2rdLYMb5VuTMfJyxvU5Tu+l/1EssQB06dIjq1auzdOlSWrduTe/evUmXLp3XZUmAUCATkYBzNPoXuoZ8z+DdFclw0wU+aLyX//W9VxeAB7CoqCiCg4M5fPgw48aNo06dOl6XJAFGfweKSMCIORlDnwqLyFPwVgburkT4c1vYvjs9HYcpjAWyMWPGULx4cYwxrFy5UmFMPKFAJiKpXkICTOq4mUeyH6LtvBd57q5f+H7REYavepy7/6uFgkAVGxtLy5YtCQ8Pp3jx4kRHR/P00097XZYEKAUyEUnVFkcep9Adu6jVLT9ZzSnmfRjFVwee4rEyd3ldmnjowIEDlClThkGDBtG2bVvmzZtH9uzZvS5LApj+NBSRVOn77+JpX+c35v94H/dxknGVI6k16WVuynyz16WJx1avXk1ISAjHjx9n8uTJhIWFeV2SiGbIRCR12b0b6lY6ylPPGNb+mIXeeYay9fsY6swKVRgThg8fTokSJciYMSOrV69WGBOfoRkyEUkVjh2D7p1jGDjkJojPTLtMg3i7793c3qgJGON1eeKxmJgYWrVqxYgRIyhXrhyTJk0iW7ZsXpcl8v8UyETEr50/D58OsHTveoETZ9JRl3F0rbOd+wa0hdtu87o88QG//fYbISEhrFmzhnfeeYeuXbuSJo1uYBDfokAmIn4pPh4mToSO7S+w90A6KrCInvnGUmBcWyj0mtfliY9YsWIFoaGhnD59msjISEJCQrwuSeSytIdMRPyKtTBvHjz9ZDz16sFdB77n6yyVmTtkDwU2TYJChbwuUXyAtZZBgwZRunRpsmbNypo1axTGxKdphkxE/EZ0NLz1luXrrw250+wlgvZUrZ+Vm3p+Bnfc4XV54iPOnTtHs2bNGDt2LJUqVWL8+PHcpuVr8XEKZCLi83buhI4dYfJkyJ7uBP3pRNPHVpN+SH8oUsTr8sSH7Nmzh+DgYKKjo+ncuTOdOnXiJl1OKn5AgUxEfNb+/fDhhzB8uCUdF3j3pj68dfNgsvZ9G5r2BW3MlkssWbKEatWqERsby6xZs6hcubLXJYlcNf3ZICI+5/ff4Z13IE8ey/BhCTTMMIHtcffzYd2fybotGlq0UBiT/2etpW/fvpQtW5bs2bOzdu1ahTHxO5ohExGfcfYsDBwIPXvC8eNQ4+6ldD3QiDwPZobBn0OxYl6XKD7m7NmzNGrUiEmTJhEUFMSYMWPImjWr12WJXDPNkImI5y5cgGHDIE8eaN8eimTbyvq0hZh0tgp5+rd2u/kVxuQvdu3aRdGiRZk8eTLdunUjMjJSYUz8lmbIRMQzCQkwdSq89x5s3w7F8h1lSkJTnt8RCXXqQK8v4O67vS5TfNDChQsJCwsjISGBOXPmUKFCBa9LErkhmiETkRRnLXz1FTzzDNSoATenieHLgl1YviU7z9+xBZYtg3HjFMbkb6y19OrVi/Lly5MjRw6ioqIUxiRVUCATkRS1ciWULAkVK8LJEwlMqBLJhp238vLWTzB9+8J330GJEl6XKT7o9OnTVK9enfbt2xMaGsqqVat48MEHvS5LJEkokIlIiti4ESpXhuLFYds2y6AmP/BTQj5qzazKTVVDYOtWeOMNSJfO61LFB23fvp3nnnuOadOm0atXLyIiIsiSJYvXZYkkGe0hE5FktXMndO7s7p3MmhW6tzlM642NyDxsFjz6KCxZAqVKeV2m+LC5c+dSs2ZN0qRJw/z583nxxRe9LkkkyWmGTESSxb59rl1YvnwQGQlvvRHDzjqd6TAwJ5nXLoG+fWHDBoUxuaKEhAQ+/PBDKlWqxAMPPEB0dLTCmKRamiETkSR1+DB89BEMGgRxcdCgvqXTY9PJ0aOVa71fvz706AF33ul1qeLDTp48Sb169Zg5cya1atVi+PDhZMqUyeuyRJKNApmIJInjx6FPH+jXD86dc10rOoVsJvdHTWD4SihUCGbMgGef9bpU8XFbtmwhKCiIbdu20a9fP1q3bo0xxuuyRJKVlixF5IacOgXdukHu3O5tpUqweeVxxtzcjNyvPg4//wyffQarVyuMyb+aNWsWhQsX5ujRoyxatIjXX39dYUwCggKZiFyXc+fcjFju3NCxo+tUsSE6noiSQ8j3ch4YMQJat3aBrH59uEn/u5ErS0hIoFOnTlSpUoWHH36Y6OhoSml/oQQQLVmKyDWJiYGRI91s2P798NJL8MEHUDhmOdRvBd9/D6VLw4AB8NhjXpcrfuD333+ndu3azJkzh/DwcAYPHkzGjBm9LkskRelPVhG5KnFxbuXxoYegZUt37+SyZTB/1G8U7l/LTZEdO+buQlq8WGFMrsrmzZspVKgQ8+fPZ/DgwXz22WcKYxKQFMhE5B/Fx8OkSfDII9CwobvNaMECWLYghhKrPoKHH4Zp09yFlD/9BFWrgvb8yFWIjIzk2Wef5fTp0yxZsoRmzZppv5gELAUyEbksa2H6dHjiCahVCzJlglmz3N78snFfYQo8Dm+/DS++CD/+CF27QubMXpctfiA+Pp4OHTpQtWpVChQoQHR0NMWLF/e6LBFPKZCJyJ9YC3PnQsGCEBLiliqnTIH166Fy/h2YVyu7iyiNcTeEz5zpdvaLXIVjx45RsWJFevbsSZMmTViyZAk5cuTwuiwRzymQiQjggtiCBVCsGLz8susrNmYMbNoE1Sqc4qZ3O/xx1VGvXu5yyvLlvS5b/Mj3339PwYIFWbp0KSNGjGDo0KFkyJDB67JEfIICmUiAsxYWLnSXfpcrB7/+CkOHwpYtUK9OAmknjHE7+Xv2hLAwdwl4u3aQPr3XpYsfmTRpEkWKFCE2NpZvvvmGhg0bel2SiE9RIBMJUNa6w5DPP+9aV+zZA0OGwLZt0KQJpI/61jVyDQ+H+++HNWtg7FjQ8pJcg7i4ON58801q1apFwYIFiY6O5lk1CBb5GwUykQBjLXz9NZQs6fbj//KLu3dy+3Zo2hQyHNoLNWu6tcv9+2HCBFi5EgoX9rp08TOHDx+mXLlyfPLJJ7Rq1YrFixdz1113eV2WiE/yLJAZY9IYY9YbY75M/DibMWahMWZb4tvbvapNJLVauhRKlYIyZWDHDvj0UxfEmjeHDPFn4f33XRuLGTNcG4utW90RS3XZl2sUHR1NwYIFWblyJWPGjGHAgAGkS5fO67JEfJaX/5d9Hfjpko/fBhZba/MCixM/FpEksGyZa55furRbkhwwwAWyli0hYwYLERGQLx906QKvvOI2kKmNhVynsWPHUqxYMQBWrlxJvXr1PK5IxPd5EsiMMf8FXgZGXvLwq8DYxPfHAlVSui6R1Gb5cnjhBTcrtmUL9OvnglirVpAxIxAd7TaR1agB2bO75DZlCuTK5XXp4ocuXLhAq1ateO211yhatChRUVE888wzXpcl4he8miHrB7wFJFzy2F3W2v0AiW/vvNw3GmMaG2OijDFRhw8fTv5KRfzQihVuf1iJEq5na9++sHMnvP463HwzcOAANGgAhQq5y79HjIB169w3iFyHgwcPUqZMGQYOHMibb77JggULuOOOO7wuS8RvpHggM8ZUAg5Za6Ov5/uttcOttQWttQX1wy7yZ99+C2XLukmvjRuhTx8XxN54IzGIxcS4HmIPPQTjx8Obb7o1zIYNIU0ar8sXP7VmzRqeeeYZoqKimDRpEr179yZt2rRelyXiV7z4iSkGVDbGVAQyAlmNMROAg8aYe6y1+40x9wCHPKhNxC+tWuW2fy1YAHfcAb17Q7Nm7rojwB2tnD3bBbAdO9w+sT59IG9eL8uWVGDkyJG0aNGCnDlzsmrVKp544gmvSxLxSyk+Q2at7WCt/a+19n4gDPjaWlsbmA1c3PlZD5iV0rWJ+JtvvnEzYkWLwnffucmvXbtc7vr/MLZpk/uiKlUgQwaYP9+FM4UxuQExMTE0adKERo0aUapUKaKiohTGRG6AL51l7wmUNcZsA8omfiwif3Gxj1ipUq6X2A8/wMcfuyDWrt0lByMPHnSNxZ54wqW1AQNgwwbXBVbkBuzbt49SpUoxfPhw3n77bebOnUu2bNm8LkvEr3m6yG+tXQosTXz/KFDGy3pEfJm1bnLrgw/cXrEcOdypyUaNLpkNAzh/3n2ie3c4d871tujUCf7zH89ql9Rj5cqVhIaGcurUKT7//HNCQ0O9LkkkVfClGTIRuQxr4Ysv3C1GFSrA3r2us/6OHe7U5J/2iV3sJ9ahg+t3sXkz9O+vMCY3zFrL4MGDKVWqFFmyZGHNmjUKYyJJSIFMxEclJMD06fDMM1C5Mhw5AsOH/9FZP2PGS7541Sq3kaxGDbj9dremOXOmO00pcoPOnz9PgwYNaNGiBS+99BLr1q0jf/78XpclkqookIn4mPh415v1iScgJAROn4bRo90tRo0aQfr0l3zxrl0QFubC2O7d7gujolxLfpEksHfvXp5//nlGjx5Np06d+OKLL7jtttu8Lksk1VGjGBEfERfnVhy7dXNd9R95BCZOhGrV4G8tnU6ccHvE+vVz/cM6d4a2bSFLFk9ql9Rp2bJlVK1alfPnzzNz5kxeffVVr0sSSbU0QybisQsX3MTWI49AnTqQLp2bIdu4EWrW/EsYi4uDIUMgTx7X46JGDddpv0sXhTFJMtZa+vfvT5kyZfjPf/7D2rVrFcZEkpkCmYhHYmPdnrCHHoL69eGWW9yesQ0b3KzY3xrnf/WVW8ds3hwefdQtTY4ZA//9rxflSyp19uxZ6tSpwxtvvMErr7zCmjVryJcvn9dliaR6CmQiKezcORg40E1yNWkCd97pTlFGR0NQENz015/KTZugfHmoWNGluBkzYOlSt9tfJAn98ssvFCtWjEmTJvHBBx8wbdo0smbN6nVZIgFBe8hEUsjJkzB4sLvo+9AhKFYMRo50TfSNucw3HDzo9oaNGAFZs7pvbN78L7v6RZLGokWLqF69OvHx8Xz55ZdUrFjR65JEAopmyESS2ZEj8N57cN99rj3YU0/BsmWwfLlrmv+3MHbmjOv+micPfPYZtGrlel288YbCmCQ5ay0ff/wx5cqVI0eOHERFRSmMiXhAM2QiyeS339z93cOGwdmzEBzsAlnBglf4hrg4tyesUyfYv999Q48e6iUmyebMmTPUr1+fqVOnUrVqVUaNGkUWHQ4R8YQCmUgS27HDHYAcM8b1FKtZE95+2+3DvyxrYe5caN/eddYvUgQ+/9ytaYokk+3btxMUFMSPP/7IRx99RLt27TCXXTsXkZSgQCaSRDZtchNaERGudUWDBu6y7wce+IdviopyX7R0KeTNC9OmuZ39+sUoyeirr76iZs2a3HTTTcybN4+yZct6XZJIwNMeMpEbtHYtVKkCjz8Os2bB//7nGugPHvwPYWzXLjd1VqiQmxUbONC9DQ5WGJNkY62le/fuvPzyy+TKlYuoqCiFMREfoRkyketgrZvU6t4dFi1y10d26eL232fL9g/feOyYa8U/cKBrNPbuu/DWW+4UpUgyOnXqFPXq1WPGjBnUrFmTESNGkOn/b6YXEa8pkIlcA2vhyy9dEFu9Gu6+Gz7+2PUTu+WWf/jG8+ddCOvWzfW/CA+H99+HnDlTrHYJXFu3biUoKIiff/6ZTz75hDfeeEP7xUR8jAKZyFWIj3f77Hv0gB9+gPvvdzcYvfYaZMz4D9+YkACTJrmZsD17XHPXnj3d+qZICpg9ezZ16tQhffr0LFy4kNK6eF7EJ2kPmcg/OHfOBa+HHnLXRl64AOPGuesjmzb9lzC2eLHrcVGnDmTP7j6eM0dhTFJEQkICXbp04dVXXyVv3rxER0crjIn4MM2QiVzG8eMuiPXv77rqP/ss9O4Nr756mauN/ur7712fi3nzIFcumDgRwsKu4htFksaJEyeoXbs2X375JfXq1WPIkCHcfPPNXpclIv9AgUzkEr/95m4oGjYMTp+GChVce7ASJa7i8OPOna6p66RJcNttbnNZy5b/Mo0mkrR+/PFHqlSpwq5duxg4cCDNmzfXfjERP6BAJgL89JPLTxMmuG1fYWGuPdgTT1zFNx88CB9+6FJc2rRuduytt1woE0lB06ZN47XXXiNz5sx8/fXXPP/8816XJCJXSYFMAtqqVfDRR65/2M03u9OSb77pNu3/q5Mn3TrmJ5+4U5SNGrlLK3PkSO6yRf4kPj6e9957jx49evDss88ybdo0cuoEr4hfUSCTgGMtfPWVO+y4fLnrG9apk1tdvOOOq3iC8+fdBrNu3eDoUahe3V0Gnjdvstcu8lfHjh2jZs2azJ8/n8aNGzNgwAAyZMjgdVkico0UyCRgXLgAU6a4eyY3boR774V+/dwVR1d1n3J8PIwfD507uxYWZcu6PhjPPJPstYtczg8//EBQUBB79+5l2LBhNG7c2OuSROQ66diXpHpnzsCAAZAnj+tAkZDgWlfs2AGvv34VYcxamD3bbSgLD4e77nLt+RcsUBgTz0RERFCkSBHOnz/PsmXLFMZE/JwCmaRaR46464xy5XLB67774IsvXGPXOnXcBeD/avlyKF7c9bu4cMF1h12zBsqUSe7yRS4rLi6Odu3aUaNGDZ5++mmio6MpUqSI12WJyA3SkqWkOjt2uNYVo0a5xq6VK7vWFUWLXsOT/PADvPOOa+SaIwcMH+5mx9LqR0a8c+TIEcLCwli8eDEtWrTgk08+IX369F6XJSJJQL9dJNVYtQr69IHp093sV+3a7sTko49ew5Ns3+6m1SZNgltvdUcwW7VyRzBFPPTdd98RHBzMgQMHGD16NK+99prXJYlIElIgE78WH++2d/XuDd9+C7ffDh06uBOT99xzDU+0d687KTlqFKRP76bU3nrLPaGIx8aPH0/jxo254447WLFiBQULFvS6JBFJYgpk4pfOnoWxY10LsO3b4YEH3Mb98PCrPDF50cGD0L07DB3qPm7RwiW6u+9OlrpFrsWFCxdo27YtAwYMoFSpUkyZMoU777zT67JEJBkokIlfOXQIBg1y/x09CoULw9SpEBR0jdu7jh1zrfkHDICYGJfk3nvP7fwX8QEHDx6kWrVqfPPNN7Rp04ZevXqRVnsYRVIt/XSLX9i61c2GjR0LsbFuo37btlCs2FXcMXmpkydd87E+feDUKahRw+0ZU1NX8SFr164lODiYY8eOMXHiRGrWrOl1SSKSzBTIxGdZ67pO9Onj9ollyACvvQZt2sDDD1/jk509C4MHu/b8R4+6KbWuXeGxx5KjdJHr9tlnn9G8eXNy5MjBt99+y5NPPul1SSKSAtSHTHxOXJxbhnz2WShZElau/KM5/tCh1xjGYmLc+maePO628IIFYd06dxRTYUx8SGxsLM2aNaNhw4aUKFGCqKgohTGRAKIZMvEZp0+7Q459+8Ivv7hVxCFDoG5dyJTpGp8sLs614+/aFXbvhhIl3L1Jzz+fHKWL3JD9+/cTGhrKt99+S/v27enWrRtp0qTxuiwRSUEKZOK53bvh009h5Eg4ccLtC+vbF155Ba75d1J8vJte69IFfv7ZzYgNH+7unbymzWYiKePbb78lNDSUkydPMmXKFKpVq+Z1SSLiAS1ZiiesdX3DqlaF3LndPvvy5V1z1xUroEqVawxjCQluBqxAAahZ0/USmzED1q6Fl15SGBOfY61l6NChlCpVikyZMrF69WqFMZEApkAmKerCBZg8GZ57zs2ELVrkTkvu2gUREe7xa5KQ4GbEChSAsDD32JQp8P33LtUpiIkPOn/+PA0bNqRZs2a8+OKLrFu3jse0p1EkoGnJUlLEsWMwYgQMHAi//ur2hw0a5PaHXVMj14sSEtzG/Pffh02b4JFHXKILDb2OdU6RlLN3715CQkJYt24dHTt2pEuXLtovJiIKZJK8tm6F/v1d/7CzZ6FMGXdSskIFuOl65mcTEtxS5Pvvw8aNkC+fu3eyWjUFMfF533zzDVWrVuXcuXPMmDGDKlWqeF2SiPgILVlKkrPWLUVWquTy0mefQfXqbhVx0SJ4+eXrCGMXg9hTT7lZsNhYmDjRzY7VqKEwJj7NWsuAAQMoU6YMt99+O2vWrFEYE5E/0QyZJJnz591kVb9+bvLqzjvdYcemTeGuu67zSa2FWbPcjNiGDW6tc/x4hTDxG+fOnaNJkyaMHz+eypUrM378eLJmzep1WSLiYxTI5IYdPOia4A8ZAocPu/31o0e7PfYZM17nk1oLX3zhEt369a6x67hxLojpPj/xE7/88gvBwcFs2LCBrl278u6773LTda3Vi0hqp99sct3WrnX9w6ZMcX1YK1Vy1xqVKnUDhxsTElwQ++ADiI6GBx+EMWOgVi0FMfErixcvpnr16sTFxfHFF1/w8ssve12SiPgw/akm1+Ti1q1nn3X/zZoFzZq5zfuzZ0Pp0tcZxi42dH3qKdeu4vhxN822ZQvUq6cwJn7DWkufPn146aWXuOuuu1i3bp3CmIj8K/2Wk6uyf787HTlsmFuifPhhNztWrx7ccssNPHFcnGtM1r27C18PP6ylSfFbZ86coWHDhkRERBASEsLo0aO55YZ+QEQkUOg3nlyRtbB6tQten3/uJrEqVoTWreHFF6+zbcVFsbFuc36PHrBjBzz+uFv7DAnRZn3xSzt27CAoKIhNmzbRo0cP2rdvj1FjYhG5Sgpk8jcxMS4bffopREVB1qzQsiW0aOH21t+Q8+fdDeIffQR79sAzz8DMme7iSm12Fj81b948atSogTGGr776inLlynldkoj4Gf0GlP/322/w3ntw771uKfLMGXd68rff3GXfNxTGzp51T5I7t0t2OXPC3Lmwbh28+qrCmPglay09evSgYsWK3HfffURFRSmMich10QxZgLt4yfeAAe4movh4N1nVqpXrqn/DKy6nTrk7kj75xPXEKFUKJky4gd3/Ir7h1KlThIeHM23aNGrUqMGIESPInDmz12WJiJ9SIAtQZ8/+sSy5fj3cdhu8/jo0b+4msW7Y8ePuyfv1c++XKwcdO0Lx4knw5CLe+vnnnwkKCmLLli306dOHNm3aaL+YiNwQBbIAs22bOy05erTLSfnzu49r14Yk+eP+4vrmsGFw+jRUrgzvvguFCyfBk4t478svv6RWrVqkT5+ehQsX8sILL3hdkoikAgpkASAuDr780nXSX7DAdZMIDnazYSVKJNHK4c8/w8cfu5YVcXGuTX/79q5tv0gqkJCQwAcffECXLl14+umnmT59Orly5fK6LBFJJRTIUrEDB2DkSDdZ9euv8N//ugb4DRrAPfck0Yt89x307AmRkZA+vXvytm2TaN1TxDecOHGCunXrMnv2bOrWrcvQoUO5+eabvS5LRFIRBbJUxlpYvtydjpw2zU1WlS3rtnNVqpREvVathaVLXRBbsMD1xWjfHt544wZuERfxTT/99BNVqlRh586dfPrpp7Ro0UL7xUQkyaV4IDPG3AuMA+4GEoDh1tr+xphswBTgfuAXoJq19nhK1+evTp50hxcHD4bNm90m/VatoGlTeOihJHqRhAR3P1LPnrBmjQtfPXu6F7n11iR6ERHfMX36dOrVq0emTJlYvHgxJUqU8LokEUmlvGj+FAe8aa19BHgOaGGMeRR4G1hsrc0LLE78WP7Fxo3uLsmcOV17r4wZ4bPP3N76Tz5JojB24QKMHQuPPQZBQXDokNuQtmuXmxlTGJNUJj4+no4dOxISEsKjjz5KdHS0wpiIJKsUnyGz1u4H9ie+f8oY8xOQE3gVKJX4ZWOBpUD7lK7PH8TEuJ5hgwfDihWQIYO7+rF5cyhUKAlf6NQp11W/Tx/Yu9dt0J80CapW1T2TkmodP36cWrVq8dVXX9GwYUMGDhxIhgwZvC5LRFI5T3+rGmPuB54C1gB3JYY1rLX7jTF3XuF7GgONAe67776UKdRH/PwzDB8OY8bA0aPw4IPQuze89hr85z9J+EL79rlNZ0OHwu+/u95hQ4dChQpq5iqp2saNGwkKCmLPnj0MGzaMxo0be12SiAQIzwKZMSYLMA14w1p78mo3yVprhwPDAQoWLGiTr0LfcHE2bPhwt48+bVp301CjRm6zfpLeOLRpk5sNmzjRtewPDoY334TnnkvCFxHxTVOnTiU8PJxbb72VZcuWUaRIEa9LEpEA4kkgM8akw4Wxidba6YkPHzTG3JM4O3YPcMiL2nzF1q0wYsQfs2EPPADdu0N4ONx9dxK+kLWwZInrITZvHmTKBE2auBOTDz6YhC8k4pvi4uJ45513+PjjjylatCiRkZHck2R9YUREro4XpywN8Bnwk7X2k0s+NRuoB/RMfDsrpWvz2sXZsGHDYNkyNxtWpQo0buzulUzS2bALF+Dzz92a5/r17sTkhx+6E5NJuv4p4ruOHj1KWFgYixYtonnz5vTt25f06dN7XZaIBCAvZsiKAXWAjcaYDYmPvYMLYlONMQ2APUBVD2rzxNatbkly7Fg3G5Y7N/To4faGJelsGLh2v4UUAAASQUlEQVT+GCNHujsm9+6FfPncx7VquSOaIgFi/fr1BAcHs3//fkaNGkV4eLjXJYlIAPPilOUK4EobxsqkZC1eOn/+j71hl86GNWkCL7yQxLNh4Fr1Dxjgpt9OnoSSJd0xzYoVk+HFRHzbhAkTaNSoEdmzZ2f58uUUStLjySIi1069C1LY5s2uT9i4cX/MhvXs6WbDkqXJ/erVbjYsMtLtF6ta1W3U1y8gCUAXLlygXbt29O/fn5IlSzJ16lTuvPOyB7pFRFKUAlkKOHkSIiJcEFu7FtKlcyclk2027MIFF8D693cd9W+91W3Sb9kS7r8/iV9MxD8cOnSIatWqsWzZMl5//XU+/vhj0qVL53VZIiKAAlmyuXin5KhRbu/82bOQP7/rnl+7NtxxRzK86NGjbg100CDXqj9vXhg4EOrVgyxZkuEFRfzDunXrCA4O5siRI4wfP57atWt7XZKIyJ8okCWxffvccuSoUbBtG9xyiwtgDRq4VcJk6au6ebObDRs/3m1OK1vW7RWrUEH7wyTgjR49mmbNmnH33Xfz7bff8tRTT3ldkojI3yiQJYELF+DLL10ImzvX3cFdogR07Aihoa61V5JLSHAv1r8/LFrkTkjWrQutW7upOJEAFxsbS5s2bRg8eDBlypQhIiKC7Nmze12WiMhlKZDdgJ9+ciFs3Dh33/Y997i7tsPD3Wphsjh50r3ggAFuCi5nTtcjo1Ej9Q8TSbR//36qVq3KypUradeuHd27dyet7l8VER+m/0NdoxMn3J6wUaNg1SrXruKVV9ySZLlyyXjn9o8/ur1h48bB6dPuOqOuXSEkxJ0SEBEAVq1aRUhICCdOnCAiIoLq1at7XZKIyL9SILsK8fFuVXDsWJgxw23TypfP3TZUp04ytasAtxY6a5YLYkuXQoYMUL06tGgBhQsn04uK+K/hw4fTsmVL7r33XubPn8/jjz/udUkiIldFgewfbN7sQtiECbB/P9x+O9Sv7w4tJtsGfXAvNmKE25i/bx/kyuWalTVoANoDI/I3MTExtGzZkpEjR1K+fHkmTZrE7bff7nVZIiJXTYHsL44cgcmTXRCLjoY0aVwz+3r1oFIlN0mVLC72yRg8GKZNg7g4twY6dKgrIE2aZHphEf/266+/Ehoaypo1a3jnnXfo2rUrafTzIiJ+RoEMiI2FOXPc9qw5c9xK4ZNPQt++ULMmJGsj79OnYeJEtyy5cSPcdhu0agXNmiXjyQCR1GH58uWEhoZy9uxZpk2bRnBwsNcliYhcl4ANZNa6GbCxY92M2NGjbi9Y69aue0SBAslcwMaNbkly/Hh3cvLJJ90yZc2aydQnQyT1sNYyaNAg2rRpQ+7cuVmyZAmPPvqo12WJiFy3gAtku3e7ADZ+vDu4mCGDu8aoXj146aVkPCUJrl3/lCmum/7q1e7FQ0OheXMoUiQZN6WJpB7nzp2jadOmjBs3jldeeYXx48dz6623el2WiMgNCYhAdvSoa1UxaZLbpgVQtKjbnlWtmtusn6wuzoZNmOD6ZuTL5+5QqltXvcNErsHu3bsJDg7mu+++4/3336djx47cpNsoRCQVSLWB7OxZ+OILtz1r3jy3L+yRR+DDD92q4AMPJHMBZ87A1Kl/nw1r0gSKF9dsmMg1WrJkCdWqVSM2NpbZs2fzyiuveF2SiEiSSVWBLC4Ovv7ahbDp091++Rw53L6wWrXcNq1kz0E//OBC2MW9YfnyudMBdepoNkzkOlhr6du3L2+99RYPPfQQM2fO5KGHHvK6LBGRJOX3gcxaiIpyISwiAg4ehKxZ3VJkrVpQsmQKdIw4edLtDRs16o/ZsKpVoXFjzYaJ3ICzZ8/SsGFDJk+eTHBwMGPGjOGWW27xuiwRkSTn14Fs3z54+GF3pWP69PDyyy6Evfyyu2s7WSUkwLJlMHo0REbCuXNuTVSzYSJJYufOnQQFBbFx40a6d+/O22+/jdEfNyKSSvl1INu/H0qXdhd6h4S4Fl7Jbvdu1ytjzBjYtctNx9Wt624UL1xYs2EiSWDBggWEhYVhrWXu3LmUL1/e65JERJKVXweyxx93e8aS3blzMHOmW5JcvNitk5YpAx98AEFB6hsmkkSstfTq1Yt33nmH/PnzM2PGDB588EGvyxIRSXZ+HcjSp0/GJ7+4OW3UKNe47MQJd6dk586uadn99yfji4sEntOnTxMeHk5kZCRhYWGMHDmSzJkze12WiEiK8OtAliz27HEnBCZMcJ1jM2Z066H160OpUqCeRyJJbtu2bQQFBfHTTz/Ru3dv/ve//2m/mIgEFAUycLNfkZGuVcWyZe6xYsVc59iwMFAXcJFkM2fOHGrVqkXatGlZsGABZcqU8bokEZEUF7iBLDYW5s93IWz2bIiJcZd5d+3qjmrmzu11hSKpWkJCAt26daNz5848+eSTTJ8+nfu1FUBEAlRgBTJrYe1aF8IiItydStmzQ6NGrlVFoUI6JSmSAk6ePEndunWZNWsWderUYdiwYdx8881elyUi4pnACGRbtrjGrRMnuqZlGTO6G8Vr14Zy5SBdOq8rFAkYW7ZsoUqVKmzfvp0BAwbQsmVL7RcTkYCXegPZzp0uhEVEuOuMjHGb8jt0gOBg7QsT8cDMmTOpW7cuGTNmZPHixZQsWdLrkkREfELqCmS//uou9I6IgHXr3GNFikD//u5i7xw5vK1PJEDFx8fTpUsXPvzwQwoVKsS0adO49957vS5LRMRn+H8gO3DAnZCcMgVWrHCPPfMM9OrlLrTMlcvb+kQC3O+//06tWrWYO3cu9evXZ9CgQWRM9rvNRET8i38Hsp9/hpw53b2Sjz0GH37oQljevF5XJiLApk2bCAoKYvfu3QwZMoQmTZpov5iIyGX4dyCLjYV334Xq1SF/fq+rEZFLfP7554SHh3PLLbewdOlSihYt6nVJIiI+y7/bzj/2mOsbpjAm4jPi4+Np37491apVo0CBAkRHRyuMiYj8C/+eIRMRn3L06FFq1KjBwoULadq0Kf379yd9sl46KyKSOiiQiUiS2LBhA0FBQezbt4+RI0fSoEEDr0sSEfEb/r1kKSI+YdKkSRQtWpQLFy6wfPlyhTERkWukQCYi1y0uLo7//e9/1KpVi0KFChEdHU3hwoW9LktExO9oyVJErsuhQ4eoXr06S5cupXXr1vTu3Zt0uoZMROS6KJCJyDWLiooiODiYw4cPM27cOOrUqeN1SSIifk1LliJyTcaMGUPx4sUxxrBy5UqFMRGRJKBAJiJXJTY2lpYtWxIeHk7x4sWJjo7m6aef9rosEZFUQYFMRP7VgQMHKFOmDIMGDaJt27bMmzeP7Nmze12WiEiqoT1kIvKPVq9eTUhICMePH2fy5MmEhYV5XZKISKqjGTIRuaIRI0ZQsmRJMmbMyOrVqxXGRESSiQKZiPxNTEwMTZo0oXHjxpQuXZp169ZRoEABr8sSEUm1FMhE5E9+++03SpUqxfDhw+nQoQNz5swhW7ZsXpclIpKqaQ+ZiPy/FStWEBoayunTp4mMjCQkJMTrkkREAoJmyEQEay2DBw+mdOnSZM2alTVr1iiMiYikIAUykQB3/vx56tevT4sWLShfvjxr164lf/78XpclIhJQFMhEAtiePXt4/vnnGTNmDJ07d2bWrFncdtttXpclIhJwtIdMJEAtWbKEatWqERsby6xZs6hcubLXJYmIBCzNkIkEGGst/fr1o2zZsmTPnp21a9cqjImIeEyBTCSAnD17ltq1a9OmTRsqV67MmjVrePjhh70uS0Qk4CmQiQSIXbt2UaxYMSZPnky3bt2IjIwka9asXpclIiJoD5lIQFi4cCFhYWEkJCQwZ84cKlSo4HVJIiJyCc2QiaRi1lp69epF+fLlyZEjB+vWrVMYExHxQT4XyIwx5Y0xW40x240xb3tdj4i/On36NGFhYbRv357Q0FBWrVpFnjx5vC5LREQuw6cCmTEmDTAIqAA8CtQwxjzqbVUi/mf79u0UKVKEyMhIevXqRUREBFmyZPG6LBERuQJf20NWGNhurd0JYIyJAF4FfrzcF69fvz5JfslYa2/4OfQ8/vc8Sflcvvg82bJlY/78+bz44otJ8pwiIpJ8fC2Q5QT2XvLxr8Czl36BMaYx0Djxw9NnzpzZmkK1XY/swBGvi/BjGr8bcOzYsexly5bV+F0f/du7MRq/G6Pxu36+Pna5rvQJXwtk5jKP/WnKwFo7HBieMuXcGGNMlLW2oNd1+CuN343R+F0/jd2N0fjdGI3f9fPnsfOpPWS4GbF7L/n4v8A+j2oRERERSRG+FsjWAXmNMQ8YY9IDYcBsj2sSERERSVY+tWRprY0zxrQE5gNpgFHW2s0el3Uj/GJp1Ydp/G6Mxu/6aexujMbvxmj8rp/fjp1JyhNrIiIiInLtfG3JUkRERCTgKJCJiIiIeEyBLAkZY24zxkQaY7YYY34yxhQxxmQzxiw0xmxLfHu713X6ImNMG2PMZmPMJmPMZGNMRo3dlRljRhljDhljNl3y2BXHyxjTIfE6sq3GmHLeVO07rjB+Hyf+7P5gjJlhjLntks9p/C5xufG75HNtjTHWGJP9ksc0fomuNHbGmFaJ47PZGNPrksc1dpe4ws/uk8aY1caYDcaYKGNM4Us+5zfjp0CWtPoD86y1+YAngJ+At4HF1tq8wOLEj+USxpicQGugoLX2MdyBjjA0dv9kDFD+L49ddrwSrx8LA/Infs/gxGvKAtkY/j5+C4HHrLUFgJ+BDqDxu4Ix/H38MMbcC5QF9lzymMbvz8bwl7EzxpTG3UpTwFqbH+id+LjG7u/G8Pd/e72A9621TwKdEj/2u/FTIEsixpisQAngMwBrbay19nfcD9nYxC8bC1TxpkKflxa42RiTFsiE6z+nsbsCa+03wLG/PHyl8XoViLDWxlhrdwHbcdeUBazLjZ+1doG1Ni7xw9W4Poig8fubK/z7A+gLvMWfG3pr/C5xhbFrBvS01sYkfs2hxMc1dn9xhfGzQNbE92/lj/6lfjV+CmRJJzdwGBhtjFlvjBlpjMkM3GWt3Q+Q+PZOL4v0Rdba33B/Ee4B9gMnrLUL0NhdqyuN1+WuJMuZwrX5m/rAV4nva/yugjGmMvCbtfb7v3xK4/fvHgKeN8asMcYsM8YUSnxcY3d13gA+Nsbsxf0u6ZD4uF+NnwJZ0kkLPA0MsdY+BZxBS2xXJXGv06vAA0AOILMxpra3VaUq/3olmfzBGPMuEAdMvPjQZb5M43cJY0wm4F3cctHfPn2ZxzR+f5YWuB14DmgHTDXGGDR2V6sZ0MZaey/QhsSVKvxs/BTIks6vwK/W2jWJH0fiAtpBY8w9AIlvD13h+wPZi8Aua+1ha+0FYDpQFI3dtbrSeOlKsqtkjKkHVAJq2T+aNGr8/t2DuD+ovjfG/IIbo++MMXej8bsavwLTrbMWSMBdkq2xuzr1cL83AD7nj2VJvxo/BbIkYq09AOw1xjyc+FAZ4Efc1U/1Eh+rB8zyoDxftwd4zhiTKfGvwjK4AxEau2tzpfGaDYQZYzIYYx4A8gJrPajPpxljygPtgcrW2rOXfErj9y+stRuttXdaa++31t6P+0X4dOL/FzV+/24m8AKAMeYhID1wBI3d1doHlEx8/wVgW+L7fjV+PnV1UirQCpho3D2cO4FwXOidaoxpgAseVT2szydZa9cYYyKB73BLRetx119kQWN3WcaYyUApILsx5legM9CTy4yXtXazMWYq7g+EOKCFtTbek8J9xBXGrwOQAVjo/i5gtbW2qcbv7y43ftbazy73tRq/P7vCv71RwKjEVg6xQL3EGVqN3V9cYfwaAf0TD4WdBxqD//3b09VJIiIiIh7TkqWIiIiIxxTIRERERDymQCYiIiLiMQUyEREREY8pkImIiIh4TIFMROQSxph3jTGbjTE/GGM2GGOe9bomEUn91IdMRCSRMaYIrlP/09baGGNMdlyTThGRZKVAJiLyh3uAI9baGABr7RGP6xGRAKHGsCIiiYwxWYAVQCZgETDFWrvM26pEJBBoD5mISCJr7WngGdzVK4eBKcaY1zwtSkQCgmbIRESuwBgTirtX8BWvaxGR1E0zZCIiiYwxDxtj8l7y0JPAbq/qEZHAoU39IiJ/yAJ8aoy5DYgDtuOWL0VEkpWWLEVEREQ8piVLEREREY8pkImIiIh4TIFMRERExGMKZCIiIiIeUyATERER8ZgCmYiIiIjHFMhEREREPPZ/uiKBptHSaw8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,7))\n",
    "plt.plot(BS_c.S_vec, BS_c.price_vec, color='red',label=\"BS curve\")\n",
    "plt.plot(Merton_c.S_vec, Merton_c.price_vec, color='blue',label=\"Merton curve\")\n",
    "plt.plot(Merton_c.S_vec, Merton_c.payoff_f(Merton_c.S_vec), color='black',label=\"Payoff\")\n",
    "plt.axis([50,190,0,120])\n",
    "plt.xlabel(\"S\"); plt.ylabel(\"price\"); plt.title(\"Merton vs Black-Scholes\")\n",
    "plt.legend()\n",
    "plt.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# References\n",
    "\n",
    "[1] Cont-Voltchkova (2005), \"Integro-differential equations for option prices in exponential Lévy models\", Finance and Stochastics, 9, 299--325.\n",
    "\n",
    "[2] Merton, R. (1976). \"Option pricing when underlying stock returns are discontinuous\", Journal of Financial Economics, 3, 125--144."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
